Avery  Architectural  and  Fine  Arts  Library 
Gift  of  Seymour  B.  Durst  Old  York  Library 


f 


53d  Congress,  ) 
3d  Session.  ) 


SENATE. 


(  Ex.  Doo. 
I   No.  12. 


IN  THE  SENATE  OF  THE  UNITED  STATES. 


LETTER 

FROM 

THE  SECRETARY  OF  WAR, 

IN  RESPONSE  TO 

Senate  resolution  of  December  10,  1894,  transmitting  the  *eport  of  the 
Board  of  Engineers  and  bridge-building  experts,  with  other  information, 
relative  to  the  subject  of  a  bridge  across  the  Hudson  River  at  New  YorJc 
City. 


December  17,  1894. — Referred  to  the  Committee  on  Commerce  and  ordered  to  be 

printed. 


War  Department, 
Washington,  D.  C,  December  14,  1894. 
Sir:  I  have  tlie  honor  to  acknowledge  the  receipt  of  the  following 
resolution  of  the  United  States  Senate,  dated  December  10,  1894: 

Resolved,  That  the  Secretary  of  War  be,  and  he  is  hereby,  requested  to  transmit 
to  the  Senate  the  report  of  the  Board  of  Engineers  and  bridge-building  experts 
appointed  under  the  act  of  Congress  entitled  *4  An  Act  to  authorize  the  New  York 
and  New  Jersey  Bridge  Companies  to  construct  and  maintain  a  bridge  across  the 
Hudson  River," between  New  York  City  and  New  Jersey,"  approved  June  7,  1894; 
and  also  the  report  of  any  board  of  engineers  which  may  have  been  appointed  by 
the  Secretary  of  War  within  the  past  five  years  to  investigate  the  subject  of  a 
bridge  across  the  Hudson  River  at  New  York  City;  and  also  to  inform  the  Senate 
what,  if  any,  action  has  been  taken  on  either  of  said  reports. 

In  reply  there  is  transmitted  herewith  a  printed  copy  of  the  report 
of  the  Board  of  Engineers  appointed  by  the  President,  dated  August 
23,  1894,  on  page  53  of  which  will  be  found  attached  a  copy  of  the 
indorsement  of  the  Secretary  of  War,  dated  December  12,  1894, 
approving  the  report. 

With  reference  to  so  much  of  the  resolution  as  calls  for  "  the  report 
of  any  board  of  engineers  which  may  have  been  appointed  by  the  Sec- 
retary of  War  within  the  past  five  years  to  investigate  the  subject  of  a 
bridge  across  the  Hudson  River  at  New  York  City,"  there  is  transmitted 
d  d  advance  copy  of  a  report  of  a  Board  of  Engineer  Officers  convened  by 
an  order  of  the  Secretary  of  War,  dated  January  27,  1894,  to  ;' investi- 
gate and  report  their  conclusions  as  to  the  maximum  length  of  span 
practicable  for  suspension  bridges,  and  consistent  with  an  amount  of 
traffic  probably  sufficient  to  warrant  the  expense  of  construction."  This 
report  is  now  in  the  hands  of  the  Public  Printer,  and  the  appendices 
are  not  yet  printed. 


2 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


In  connection  with  the  subject  there  is  forwarded  a  copy  of  a  joint 
letter  from  the  president  of  the  New  York  and  New  Jersey  Bridge  Com- 
pany of  New  York  and  the  president  of  the  New  York  and  New  Jersey 
Bridge  Company  of  New  Jersey,  dated  November  21, 1894.  A  copy  of 
the  reply  of  the  Secretary  of  War  to  this  communication,  dated  Decem- 
ber 12,  1894,  is  also  herewith. 

Very  respectfully,  Daniel  S.  Lamont, 

Secretary  of  War. 

The  President  op  the  United  States  Senate. 


[The  New  York  and  New  Jersey  Bridge  Company,  office  of  the  president,  214  Broadway.   New  York 
and  New  Jersey  Bridge  Company,  80  Broadway,  City.] 

New  York,  November  21, 1894. 

Dear  Sir  :  The  New  York  and  New  Jersey  Bridge  Companies,  after 
a  careful  consideration  of  the  conditions  involved  in  the  construction 
of  a  bridge  crossing  the  North  Biver  between  Fifty-ninth  and  Sixty- 
ninth  streets,  have  become  convinced  that,  in  order  to  perfect  a  sound 
financial  basis  for  the  enterprise,  it  is  essential  that  a  guaranteed  esti- 
mate of  cost  should  be  obtained  from  parties  whose  reputation  and 
experience  in  the  construction  of  large  works  would  insure  the  accuracy 
of  their  estimates  and  the  practicability  of  the  plans  selected  by  them. 

In  accordance  with  this  view,  the  New  York  and  New  Jersey  Bridge 
Companies  have  entered  into  a  contract  with  the  Union  Bridge  Com- 
pany, whereby  the  Union  Bridge  Company  are  to  furnish  plans  and 
construct  a  cantilever  railroad  bridge  across  the  Hudson  Biver,  having 
a  main  span  not  exceeding  2,000  feet,  at  a  total  cost  guaranteed  by  the 
Union  Bridge  Company  not  to  exceed  $22,000,000,  including  interest 
charges  growing  due  during  construction,  and  to  render  such  assist- 
ance as  may  be  in  their  power  in  securing  the  necessary  capital  for  the 
completion  of  the  bridge. 

This  contract  is  of  course  expressed  to  be  conditional  upon  the 
approval  by  the  honorable  Secretary  of  War  of  the  plan  for  a  canti- 
lever bridge  having  a  main  span  not  exceeding  2,000  feet. 

Under  this  contract  the  Union  Bridge  Company  has  presented  gen- 
eral plans  and  estimates  for  a  u cantilever"  bridge,  having  a  span  of 
2,000  feet  in  the  clear,  and  is  prepared  to  execute  the  work  at  a  price 
which  it  is  believed  will  prove  remunerative  to  the  capital  invested. 

These  plans  and  estimates,  together  with  the  reports  accompanying 
the  same,  have  been  accepted  and  adopted  by  the  New  York  and  New 
Jersey  Bridge  Companies,  and  with  your  kind  permission  will  be  pre- 
sented for  your  consideration. 

The  New  York  and  New  Jersey  Bridge  Companies  are  satisfied  that 
a  "suspension"  bridge  spanning  the  North  River  without  a  pier  would 
involve  such  elements  of  uncertainty  as  regards  first  cost,  novelty  in 
its  magnitude  as  a  hitherto  untried  engineering  feat  and  time  of  con- 
struction, to  say  nothing  of  the  well-founded  prejudice  against  the 
"suspension"  principle  for  railroad  purposes,  as  would  render  the 
enterprise  impracticable  from  a  financial  standpoint. 

On  the  other  hand,  we  firmly  believe  that  the  "cantilever"  plan  pre- 
sented by  the  Union  Bridge  Company  can  be  executed  within  practi- 
cable limits  of  time  and  cost,  and  that  when  finished  the  bridge  will  be 
capable  of  fully  meeting  the  demands  of  the  heaviest  railroad  traffic. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


3 


In  addition  to  the  records  contained  in  the  printed  report  of  the 
Board  constituted  under  the  act,  a  further  report  of  Mr.  Macdonald, 
approved  by  us,  is  herewith  presented,  giving  in  detail  some  of  our 
reasons  for  considering  the  "suspension"  bridge  impracticable. 

In  view  of  the  foregoing  facts,  we  respectfully  request  that  the  canti- 
lever bridge,  with  a  main  span  not  exceeding  two  thousand  feet,  upon 
the  plans  prepared  by  the  Union  Bridge  Company,  may  receive  your 
favorable  consideration  and  decision. 

Respectfully  submitted. 

John  B.  Kerr, 
Presdt.  of  New  York  and  New  Jersey  Bridge  Go.  of  Neic  York. 

H.  M.  Haar, 

Presdt.  of  New  York  and  New  Jersey  Bridge  Co.  of  New  Jersey. 

The  Secretary  of  War, 

Washington,  D.  G. 


War  Department, 
Washington,  December  12,  1894. 

Gentle:\ien  :  I  beg  to  acknowledge  receipt  of  your  letter  of  the  21st 
ultimo,  by  which  it  appears  that  your  company  has  entered  into  a  pro- 
visional contract  with  the  Union  Bridge  Company  for  the  construction 
of  a  cantilever  bridge  between  Xew  York  and  Xew  Jersey  on  plans 
involving  the  erection  of  a  pier  within  the  lines  of  the  navigable  waters 
of  the  harbor  of  Xew  York. 

The  present  Congress,  at  its  first  session,  passed  an  act  which  would 
have  permitted  the  construction  of  a  bridge  such  as  you  now  propose. 
After  much  consideration  and  a  public  hearing,  where  representations 
of  the  commercial  organizations  speaking  for  the  vast  interests  of  the 
commerce  of  that  port  affecting  all  sections  of  the  country  were  sub- 
mitted and  the  public  demands  for  quick  and  convenient  transit  over 
the  river  at  this  point  were  expressed,  that  bill  failed  to  receive 
Executive  sanction,  and  was  returned  to  the  House  of  Representatives 
where  it  originated. 

The  reasons  for  disapproval  were  stated  in  part  in  the  veto  message, 
as  follows: 

This  bill  authorizes  the  construction  of  a  bridge  over  the  North  River  between  the 
States  of  New  York  and  New  Jersey,  the  terminus  of  which  in  the  city  of  New  York 
shall  not  be  below  Sixty-sixth  street.  It  contemplates  the  construction  of  a  bridge 
upon  piers  placed  in  the  river ;  no  mention  is  made  of  a  single  span  crossing  the  entire 
river,  nor  is  there  anything  in  the  bill  indicating  that  it  was  within  the  intention  of 
the  Congress  that  there  should  be  a  bridge  built  without  piers.  I  am  by  no  means 
certain  that  the  Secretary  of  War,  who  is  invested  by  the  terms  of  the  bill  with  con- 
siderable discretion  so  far  as  the  plans  for  the  structure  are  concerned,  would  have 
the  right  to  exact  of  the  promoters  of  this  enterprise  the  erection  of  a  bridge  span- 
ning the  entire  river. 

Much  objection  has  been  made  to  the  location  of  any  piers  in  the  river  for  the  reason 
that  they  would  seriously  interfere  with  the  commerce  which  seeks  the  port  of  New 
York  through  that  channel.  It  is  certainly  very  questionable  whether  piers  should 
be  permitted  at  all  in  the  North  River  at  the  point  designated  for  the  location  of 
this  bridge.  It  seems  absolutely  certain  that  within  a  few  years  a  great  volume 
of  shipping  will  exteud  to  that  location  which  will  be  seriously  embarrassed  by  such 
obstructions. 

I  appreciate  fully  the  importance  of  securing  some  means  by  which  railroad  traffic 
can  cross  the  river,  and  no  one  can  fail  to  realize  the  serious  inconvenience  to  travel 
caused  by  lack  of  facilities  of  that  character.  At  the  same  time  it  is  a  plain  dictate 
of  wisdom  and  expediency  that  the  commerce  of  this  river  be  not  unnecessarily  inter- 
fered with  by  bridges,  or  in  any  other  manner. 


4 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


Engineers  whose  judgment  upon  the  matter  can  not  be  questioned,  including  the 
engineer  of  the  company  proposing  to  build  this  bridge,  have  expressed  the  opinion 
that  the  entire  river  can  be  spanned  safely  and  effectively  by  a  suspension  bridge, 
or  a  construction  not  needing  the  use  of  piers. 

The  company  to  which  the  permission  to  bridge  the  river  is  granted  in  the  bill 
under  consideration  was  created  by  virtue  of  an  act  of  the  legislature  of  the  State 
of  New  York,  which  became  a  law,  by  reason  of  the  failure  of  the  governor  to  either 
approve  or  veto  the  same,  on  the  30th  day  of  April,  1890.  It  may  be  safely  assumed 
that  the  members  of  the  legislature  which  passed  this  law  knew  what  was  necessary 
for  the  protection  of  the  commerce  of  the  city  of  New  York,  and  had  informed, 
themselves  concerning  the  plan  of  a  bridge  that  should  be  built  in  view  of  all  the 
interests  concerned.  By  paragraph  24  of  the  law  creating  this  company  it  is  pro- 
vided that  "the  said  bridge  shall  be  constructed  with  a  single  span  over  the  entire 
river  between  towers  or  piers  located  between  the  span  and  the  existing  pier-head 
lines  in  either  State,"  and  "  that  no  pier  or  tower  or  other  obstruction  of  a  permanent 
character  shall  be  placed  or  built  in  the  river  between  said  towers  or  piers  under 
this  act." 

In  view  of  such  professional  judgment,  and  considering  the  interests  which  would 
be  interfered  with  by  the  location  of  piers  in  the  river,  and  having  due  regard  to 
the  judgment  of  the  legislature  of  the  State  of  New  York,  it  seems  to  me  that  a 
plan  necessitating  the  use  of  piers  in  the  bed  of  the  river  should  be  avoided.  The 
question  of  increased  expense  of  construction  or  the  compromise  of  conflicting 
interests  should  not  outweigh  the  other  important  considerations  involved. 

This  message  was  referred  to  the  Committee  on  Interstate  and  For 
eign  Commerce,  and  subsequently  a  bill  was  introduced  "intended  to 
conform  to  and  meet  the  objections  urged  by  the  President."  In  pre- 
senting this  substitute  bill  to  the  favorable  consideration  of  Congress 
that  committee  submitted  a  report  which  I  am  justified  in  assuming 
clearly  shows  the  purpose  of  Congress  in  its  subsequent  legislation 
upon  this  subject,  and  from  which  I  make  the  following  extracts: 

The  main  objection  urged  by  the  President  to  the  bill  heretofore  passed  was  that 
it  allowed  a  bridge  to  be  built  with  a  pier  in  the  river.    *    *  * 

The  bill  as  now  presented  directs  the  President  to  create  a  board  of  five  competent, 
practical,  disinterested,  expert  bridge  engineers,  of  whom  one  shall  be  a  member  of 
the  Corps  of  Engineers,  United  States  Army,  and  the  others  from  civil  life,  who 
shall,  in  the  time  stated,  meet,  investigate  and  examine  into,  determine  and  decide,  at 
what  length  of  span  not  less  than  two  thousand  feet  a  safe,  practicable  railroad  bridge 
can  be  constructed,  and  make  their  determination  as  to  the  length  of  the  span 
final.  As  this  is  the  chief  difference  between  the  executive  and  legislative  depart- 
ments in  the  passage  of  a  bill  to  bridge  the  Hudson  River,  which  is  not  only  a 
question  of  State  but  of  national  importance,  there  can  be  no  better  plan  devised 
or  determined,  at  what  span  the  river  can  be  safely  bridged,  than  by  a  board  of  the 
character  described  in  the  act  and  appointed  under  the  authority  of  the  President. 

Bridge-building  is  a  science  which  has  advanced  probably  as  much  as  any  other 
within  the  last  twenty  years.  What  was  impracticable  twenty  years  ago  is  practi- 
cable now;  what  could  not  be  safely  done  twenty  years  ago  may  be  safely  done  now, 
and  there  is  no  more  accurate  way  of  ascertaining  what  can  be  scientifically  done, 
from  a  practical  standpoint,  than  the  one  proposed  in  the  bill  for  ascertaining  what 
length  of  span  can  be  made,  taking  into  consideration  all  the  possibilities  of  the 
weight  and  strain  on  the  steel  of  which  it  is  to  be  constructed.  It  is  far  safer,  in 
the  opinion  of  the  committee,  to  leave  this  important  question  to  disinterested  expert 
bridge- builders  to  be  selected  by  the  President  than  even  to  the  opinion  of  the  engi- 
neers of  the  War  Department,  however  able  they  may  be  in  other  branches  or  other 
lines  of  engineering.  These  questions  will  be  familiar  to  the  commission.  They  have 
dealt  with  many  such  problems,  having  in  mind  not  only  the  possibility  of  length  of 
span,  but  also  the  obstruction  which  may  occur  to  the  navigation  of  the  river.  And 
their  opinion  is  certainly,  when  disinterestedly  expressed,  the  most  valuable  verdict 
which  can  be  finally  rendered  in  settlement  of  a  dispute  in  a  matter  of  this  character. 

It  will  be  seen  that  *  *  *  all  plans  for  the  construction  of  the  bridge  as  to 
length  of  span  must  conform  to  the  decision  of  this  board. 

The  committee  are  satisfied  that  if,  in  the  opinion  of  the  board  of  competent  engi- 
neers established  under  the  act,  a  safe  and  practicable  bridge  can  be  built  of  a  greater 
length  than  2,000  feet,  as  shown  in  the  plans  of  the  bridge  companies  exhibited  to 
the  committee,  they  will,  as  they  must,  adopt  it. 

They  do  not  believe  that  any  better  or  more  reliable  way  can  be  found  than  to 
leave  it  to  a  settlement  by  a  board  of  competent  engineers,  selected  by  the  President 
himself,  and  sitting  under  the  direction  of  the  Secretary  of  War. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


5 


The  act,  as  thus  presented,  was  passed  by  both  Houses,  and  was 
approved  by  the  President  June  7,  1894.  Under  its  provisions  the 
President  appointed  Maj.  Charles  W.  Raymond,  of  the  Corps  of  Engi- 
neers, United  States  Army;  Prof.  William  H.  Burr,  of  Columbia  Col- 
lege ;  G.  Bouscaren,  of  Cincinnati ;  George  S.  Morison,  of  Chicago ;  and 
Theodore  Cooper,  of  Xew  York,  "as  a  board  of  competent,  disinterested 
engineers  to  examine  and  recommend  what  length  of  span  not  less  than 
two  thousand  feet  would  be  safe  and  practicable  for  a  railroad  bridge 
to  be  constructed  over  said  river."  After  a  thorough  investigation 
covering  every  phase  of  the  problem  this  Commission  submitted  an 
exhaustive  report,  signed  by  all  of  its  members,  which  closed  with  the 
following  recommendation : 

The  only  subject  referred  to  your  Board  is  "to  recommend  what  length  of  span 
not  less  than  2,000  feet  would  be  safe  and  practicable  for  a  railroad  bridge  to  be  con- 
structed over  the  Hudson  River  between  Fifty-ninth  and  Sixty-ninth  streets."  A 
single  span  from  pier-head  to  pier-head,  built  on  either  the  cantilever  or  suspension 
principle,  would  be  safe.  The  estimated  cost  of  the  3,100-foot  clear-span  cantilever 
being  about  twice  that  of  the  shorter  span,  your  Board  consider  themselves  justified 
in  pronouncing  it  impracticable  on  financial  grounds.  As  the  cost  of  the  single- 
span  suspension  bridge  is  at  most  (not  more  than)  one-third  greater  than  that  of 
the  2,000  cantilever,  your  Board  are  unable  to  say  that  such  greater  cost  is  enough 
to  render  the  suspension  bridge  impracticable. 

The  Board  have  reached  this  conclusion  after  careful  study,  and  they  have  thought 
it  best  to  give  the  full  course  of  reasoning  which  they  have  followed.  They  feel 
that  the  contingency  attending  the  construction  of  the  deep-river  foundation  of  the 
cantilever  bridge,  even  waiving  the  absolute  necessity  of  carrying  this  foundation 
to  rock,  is  enough  to  balance  a  part  of  the  greater  cost  of  the  suspension  bridge. 

The  conclusion  of  this  Board  is  that  of  a  Board  of  Bridge  Engineers  acting  in  a 
professional  capacity.  While  from  such  professional  view  they  must  pronounce 
the  suspension  bridge  practicable,  they  do  not  in  this  conclusion  give  an  opinion  on 
the  financial  practicability  and  merit  of  either  plan. 

This  finding  is  confirmed  and  strengthened  by  the  unanimous  report 
of  a  Board  of  Officers  of  the  Corps  of  Engineers  of  the  United  States 
Army,  appointed  prior  to  the  legislative  provision  for  a  Board,  with 
instructions  to  ''investigate  and  report  their  conclusions  as  to  the 
maximum  length  of  span  practicable  for  suspension  bridges  and  con- 
sistent with  an  amount  of  traffic  probably  sufficient  to  warrant  the 
expense  of  construction." 

The  conclusion  of  this  Board,  which  is  indorsed  by  the  Chief  of 
Engineers  of  the  United  States  Army,  has  been  reported  to  me  as 
follows : 

The  final  plans  for  a  work  of  such  magnitude  would  only  be  adopted  after  the 
most  extended  tbeoretical  and  experimental  investigations,  and  the  estimated  cost 
would  undoubtedly  be  much  reduced  by  such  studies.  Assuming  the  most  favorable 
location  and  the  most  competent  engineering  management,  the  Board  believe  that 
$23,000,000  is  a  reasonable  estimate  for  a  six-track  railroad  suspension  bridge  3,200 
feet  long,  and  they  consider  the  amount  of  traffic  which  such  a  bridge  would  accom- 
modate sufficient  to  warrant  the  expense  of  construction.  They  believe,  however, 
that  the  bridge  should  be  so  constructed  that  its  capacity  can  be  readily  increased, 
and  with  the  suspension  system  this  can  be  provided  for  by  giving  suitable  dimen- 
sions to  the  towers  and  anchorages. 

If  sufficient  inducements  were  offered  to  competent  engineers  to  prepare  competi- 
tive designs  and  estimates  for  a  single-span  bridge  at  this  locality,  the  Hoard  do  not 
doubt  that  perfectly  satisfactory  plans  would  be  obtained  within  the  limit  of  co^t  of 
the  estimate  given  above. 

Briefly  stated,  the  finding  of  the  engineers  is  that  both  the  2,000-foot 
cantilever  bridge  wnich  requires  a  pier  in  the  river,  and  the  3,100-foot 
in  the  clear  suspension  bridge  without  a  center  pier  are  safe  and  not 
impracticable  as  to  cost,  the  estimates  being  as  follows: 


G 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


PIER  BRIDGE  (CANTILEVER)  SIX  TRACKS. 
[Clear  span,  2,000  feet.] 


Total  length,  4,320  feet;  moving  load,  3,000  pounds  per  foot  of  track. $25, 443,  000 
Total  length,  including  necessary  viaduct,  making  it  equal  in  length 

to  a  suspension  bridge  having  a  clear  span  of  3,200  feet,  5,600  feet; 

moving  load,  3,000  pounds  per  foot  of  track   26,  723,  000 

SUSPENSION  BRIDGE,  SIX  TRACKS. 

[Clear  span,  3,200  feet;  total  length,  5,600  feet.] 

Moving  load,  3,000  pounds  per  foot  of  track   $35,  367, 671 

Moving  load,  1,500  pounds  per  foot  of  track;  strain  on  cables,  60,000 

pounds  per  square  inch   30,  743,  000 

Moving  load,  1,500  pounds  per  foot  of  track;  strain  on  cables,  50,000 

pounds  per  square  inch   31,  671,  000 

Location  near  Sixty-ninth  street,  moving  load,  3,000  pounds  per  foot  of 

track   31, 917, 671 

Location  near  Sixty-ninth  street,  moving  load,  1,500  pounds  per  foot  of 

track   27,771,000 

Location  near  Sixty-ninth  street  (Army  Engineer  Board),  moving  load, 

1,500  pounds  per  foot  of  track   23,  000,  000 


And  I  am  further  assured  by  members  of  the  Commission  that  the 
time  required  for  construction  would  be  approximately  the  same. 

In  view,  therefore,  of  these  facts  and  findings,  and  of  the  very  serious 
objections  to  a  pier  in  the  harbor,  with  its  attendant  delay  and  constant 
menace  to  navigation,  I  am  constrained  to  require  that  the  bridge  to  be 
built  by  the  New  York  and  New  Jersey  Bridge  Companies  across  the 
Hudson  Eiver  shall  have  a  single  span  between  the  pier  lines  of  the 
harbor  of  New  York. 

While  I  do  not  undertake  w  say  that  the  objection  of  an  obstruction 
in  the  harbor  is  sufficiently  grave  to  prohibit  the  construction  of  a  pier 
bridge,  were  a  suspension  bridge  impracticable,  it  is  a  matter  for  public 
congratulation  that  a  scientific  investigation  of  the  subject  by  skilled 
and  experienced  engineers  determines  that  both  the  traffic  on  the  river 
as  well  as  that  over  it  can  be  accommodated  without  interference  and 
the  rights  of  all  protected  with  only  such  an  increase  of  expense,  if 
any,  as  is  clearly  demanded  by  the  conceded  advantages  to  follow. 
Very  respectfully, 

Daniel  S.  Lamont, 

Secretary  of  War. 

Mr.  John  B.  Kerr, 

Presdt.  of  New  York  and  New  Jersey  Bridge  Co.  of  Neiv  York. 
and 

Mr.  H.  M.  Haar, 

Presdt.  of  New  York  and  New  Jersey  Bridge  Co.  of  New  Jersey, 


Office  of  the  Chief  of  Engineers, 

United  States  Army, 
Washington,  D.  C,  October  35,  1894. 
Sir:  I  have  the  honor  to  submit  herewith  a  printed  copy  of  the 
report  of  the  Board  of  Engineer  Officers  convened  in  accordance  with 
your  order,  dated  January  :27, 1894,  to  investigate  and  report  their  con- 
clusions as  to  the  maximum  length  of  span  practicable  for  suspension 
bridges.  The  report  is  a  very  valuable  one,  shows  careful  research, 
and  I  approve  and  concur  in  its  conclusions. 

Very  respectfully,  your  obedient  servant, 

Thos.  Lincoln  Casey, 
Brig.  Gen.,  Chief  of  Engineers. 

Hon.  Daniel  S.  Lamont, 

Secretary  of  War. 
*  7 


REPORT 

OF 

BOARD  OF  ENGINEER  OFFICERS  TO  MAKE  INVESTI- 
GATIONS OF  CERTAIN  BRIDGES. 


United  States  Engineer  Office, 
Philadelphia,  Pa.,  September  29,  1894. 

General  :  The  Board  of  Officers  of  the  Corps  of  Engineers  appointed 
by  Special  Orders  No.  5,  current  series,  Headquarters  Corps  of  Engi- 
neers, U.  S.  Army,  January  29,  1894,  to  make  investigations  as  to  cer- 
tain bridges,  in  accordance  with  instructions  of  the  Secretary  of  War, 
have  the  honor  to  submit  the  following  report: 

The  instructions  of  the  Board  are  contained  in  a  letter  from  the  Sec- 
retary of  War  to  the  Chief  of  Engineers,  dated  January  27,  1894,  and 
in  the  indorsement  of  the  Chief  of  Engineers  thereon,  dated  January 
30,  1894.  Copies  of  this  letter  and  the  orders  convening  the  Board  are 
appended  hereto. 

The  Secretary  of  War,  in  his  letter  of  January  27, 1894,  remarks  that, 
"  in  view  of  the  importance  of  questions  arising  in  this  Department  in 
connection  wi&li  the  building  of  bridges  over  navigable  streams,  it  is 
essential  that  it  should  be  possessed  of  accurate  and  full  information 
necessary  to  their  intelligent  and  proper  determination and  directs 
the  formation  of  u  a  Board  of  Officers  of  the  Engineer  Corps,  who  shall 
investigate  and  report  their  conclusions  as  to  the  maximum  length  of 
span  practicable  for  suspension  bridges  and  consistent  with  an  amount 
of  traffic  probably  sufficient  to  warrant  the  expense  of  construction." 

The  indorsement  of  the  Chief  of  Engineers  of  January  30, 1894,  directs 
the  Board  to  include  in  its  investigations  u  strength  of  materials,  loads, 
foundations,  wind  pressure,  oscillations,  and  bracing." 

The  Board  convened  at  Kew  York  City  on  February  13,  1894,  and 
remained  in  session  until  February  15,  1894,  when  it  adjourned  to 
collect  information.  The  Board  held  a  session  at  Philadelphia,  Pa., 
from  March  6  to  10,  1894.  An  extended  preliminary  investigation  of 
the  subject  under  consideration  had  already  been  made  when  a  Board 
of  expert  bridge  engineers  was  appointed  by  the  President,  on  June 
15.  1894,  under  the  provisions  of  the  act  approved  June  7.  1894.  to 
recommend  what  length  of  span,  not  less  than  2,000  feet,  would  be 
safe  and  practicable  for  a  railroad  bridge  to  be  constructed  across 
the  Hudson  Biver  between  Xew  York  City  and  the  State  of  Xew 
Jersey.  The  Xew  tork  Board  was  composed  of  five  engineers,  four 
of  whom  were  civil  engineers  of  long  and  varied  experience  in  the 
designing  and  construction  of  bridges  and  of  the  highest  profes- 

9 


10 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


sional  standing.  It  was  therefore  considered  desirable  to  delay  the 
completion  of  this  report  nntil  the  determinations  of  the  New  York 
Board  could  be  ascertained  and  studied.  The  present  Board  has 
derived  much  assistance  from  the  published  report  of  the  New  York 
Board,  as  will  be  indicated  below.  At  the  last  session,  which  was 
held  at  Philadelphia  from  September  20  to  September  29,  1894,  this 
report  was  unanimously  adopted. 

The  question  of  the  maximum  practicable  span  may  be  investigated 
as  a  purely  engineering  problem,  when  certain  preliminary  conditions 
are  established.  The  bridge  will  doubtless  be  a  railroad  bridge,  since 
with  the  largest  span  the  traffic  capacity  would  not  otherwise  justify 
the  cost.  This  assumed,  the  width,  must  be  at  least  sufficient  to  accom- 
modate a  double  track.  The  number  of  double  tracks  required  must 
be  established  so  as  to  give  a  traffic  capacity  "probably  sufficient  to 
warrant  the  expense  of  construction." 

The  New  York  and  Brooklyn  bridge,  the  longest  suspension  bridge 
yet  constructed,  consists  in  reality  of  two  similar  bridges  suspended 
side  by  side  and  braced  together,  the  promenade  being  supported 
between  the  bridges  as  an  extra  weight  on  the  interior  cables.  Follow- 
ing this  idea,  the  Board  in  its  preliminary  investigation  assumed  a 
double- track  railroad  bridge  as  the  unit  bridge,  bracing  together  side 
by  side  as  many  such  bridges  as  were  considered  necessary  to  accom- 
modate the  traffic  contemplated.  The  engineering  problem  was  thus 
limited  to  the  question  of  determining  the  maximum  span  for  a  double- 
track  railroad  bridge.  It  was  found,  however,  that  there  are  many 
serious  practical  objections  to  such  an  arrangement  in  a  long-span 
bridge  carrying  very  heavy  loads.  In  this  investigation,  therefore,  the 
loads  will  be  assumed  to  be  supported  by  only  two  sets  of  cables,  one 
on  each  side  of  the  bridge;  an  arrangement  whioh  was  adopted  as  a 
basis  of  estimate  by  the  New  York  Board. 

In  the  various  projects  for  long-span  bridges  across  the  Hudson  Biver 
at  New  York  the  least  traffic  capacity  assumed  was  six  tracks,  and  the 
New  York  Board  adopted  this  number  of  tracks  in  its  investigations. 
In  this  report,  therefore,  it  is  proposed  to  first  consider  the  question  of 
the  maximum  span  for  a  six-track  railway  bridge  as  an  engineering 
problem,  after  which  the  relations  between  span,  traffic,  and  cost  of 
construction  will  receive  such  investigation  as  the  nature  of  the  sub- 
ject will  permit. 

Since  much  of  the  information  with  reference  to  strength  of  materials, 
loads,  etc.,  collected  by  the  Board  as  directed  by  the  Chief  of  Engi- 
neers, is  necessary  for  the  proper  investigation  of  the  question  of  the 
practical  maximum  span,  this  part  of  the  subject  will  first  receive 
attention. 

STRENGTH  OF  MATERIALS. 

The  supporting  cables  of  a  suspension  bridge  of  long  span  are  made 
of  steel.  They  are  either  chains  composed  of  connected  links  or  cables 
formed  of  parallel  wires  or  twisted  wire  ropes.  To  obtain  the  longest 
span  possible  the  weight  of  the  cable  must  be  a  minimum  as  compared 
with  its  carrying  capacity.  The  connections  of  a  series  of  links  add 
from  20  to  25  per  cent  to  the  dead  weight  of  the  chain,  while  in  the 
wire  cable  the  connections  add,  at  most,  only  2  or  3  per  cent.  More- 
over, steel  in  the  form  of  wire  has  a  minimum  strength  more  than  double 
its  maximum  strength  in  the  form  of  bars  suitable  for  the  construction 
of  a  suspension  chain.    A  link  chain,  therefore,  will  weigh  about  two 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


11 


and  one-half  times  as  much  as  a  wire  cable  of  equal  carrying  capacity; 
or  in  other  words,  a  wire  cable  can  be  stretched  about  two  and  one-half 
times  as  far  as  a  steel  chain  before  being  broken,  other  conditions 
being  the  same  in  both  cases.  Moreover,  it  is  stated  by  Melan*  that 
considerable  bending  moments  are  sometimes  produced  by  the  friction 
between  the  links  of  chains,  but  the  effects  due  to  the  stiffness  of  cables 
are  so  small  that  they  may  be  neglected.  It  is  therefore  assumed  that 
the  cables  are  made  of  steel  wires  laid  parallel  to  each  other. 

The  strength  of  the  suspension  cable  will  depend  upon  the  tensile 
strength  of  the  steel  employed  in  its  construction  and  upon  the  num- 
ber of  wires  it  contains.  The  wire  employed  in  the  cables  of  the  New 
York  and  Brooklyn  bridge  had  a  tensile  strength  of  170,000  pounds 
per  square  inch,  and  the  cables  were  originally  designed  to  contain 
each  6,188  wires  of  No.  7,  B.  W.  G.,  but  as  some  heavier  wires  were 
introduced  during  construction,  the  actual  number  of  wires  was  only 
5,100.  These  are  the  largest  cables  made  up  to  the  present  time,  hav- 
ing a  diameter  of  15|  inches.  The  cables  of  the  Cincinnati  suspen- 
sion bridge  have  a  diameter  of  12  inches  and  each  contains  5,200  No. 
9  wires. 

There  is  a  practical  limit  to  the  number  of  wires  which  can  be 
united  in  a  cable,  since  as  the  number  increases  it  becomes  more  and 
more  difficult  to  adjust  the  Avires  so  that  each  will  bear  its  due  propor- 
tion of  stress  under  the  varying  conditions  of  temperature  and  load- 
ing. No  unusual  difficulties,  hoAvever,  were  encountered  in  the  manu- 
facture of  the  cables  above  referred  to,  but  it  is  believed  that  with  the 
method  employed  for  making  the  cables  of  the  East  Eiver  bridge  the 
practical  limit  of  the  number  of  wires  was  very  nearly,  if  not  quite, 
attained.  With  improved  methods  the  construction  of  much  larger 
cables  might  be  found  practicable.  An  increase  in  the  size  of  the 
wire  does  not  materially  increase  the  difficulty  of  construction.  No.  3 
wire  having  a  tensile  strength  of  180,000  pounds  per  square  inch,  can 
now  be  readily  obtained  at  a  reasonable  price.  Indeed  steel  wire  much 
stronger  than  tnis  can  be  obtained  (up  to  more  than  300,000  pounds 
per  square  inch)  but  its  present  cost  would  prohibit  its  employment. 

The  Board  therefore  assumes  for  the  purposes  of  this  investigation 
a  suspension  cable  formed  of  6,000  parallel  steel  wires,  No.  3,  B.  W. 
G.  The  area  of  its  cross-section  will  be  1316  square  inches  without 
wrapping,  and  its  breaking  tensile  strength  will  be  56,880,000  pounds, 
or  1:8,410  tons.  With  a  safety  factor  of  3,  Avhich  was  adopted  by  the 
New  York  Board,  and  will  be  adopted  in  this  investigation  for  reasons 
to  be  given  hereafter,  the  working  strength  of  this  cable  will  be 
18,900,000  pounds  or  9,180  tons.  Its  diameter  with  wrapping  will  be 
21i  inches.  The  New  York  Board  have  adopted  a  cable  of  about  this 
size  and  strength  in  their  estimates. 

The  total  cable  strength  available  for  the  support  of  the  bridge 
depends  upon  the  number  of  cables  which  can  be  practically  combined 
as  a  single  cable  system  on  one  side  of  the  bridge.  If  many  cables  are 
employed  it  becomes  difficult  to  distribute  the  strains  among  them  so 
that  each  shall  carry  its  proportionate  load  under  the  varying  condi- 
tions of  temperature  and  traffic.  It  is  not  easy  to  decide  what  is  the 
practical  limit  of  the  number  of  cables  to  be  assembled  together. 
Where  parallel  wire  cables  are  used  they  must  be  sufficiently  separated 
horizontally  and  vertically  to  give  room  for  the  operation  of  the  wire- 


*HaiKlbucb  der  Ingenieurwissenschaften.  Band  n.  Der  Briickenbau — J.  Melan, 
Leipzig,  1888. 


12 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


wrapping  machine  and  this  requires  intervals  of  at  least  3  feet  during 
construction. 

The  cables  may  cross  the  saddles  on  top  of  the  towers  side  by  side  or 
they  may  be  arranged  in  one  or  more  vertical  or  nearly  vertical  planes. 
In  the  first  case  the  cradling  of  the  cables  in  converging  planes  (which 
is  desirable  for  lateral  stability),  requires  considerable  intervals 
between  the  saddles.  In  the  investigations  of  the  New  York  Board  an 
interval  of  20  feet  was  found  to  be  necessary  for  such  an  arrangement. 
But  the  cables  on  one  side  of  the  bridge  may  also  be  arranged  side  by 
side  in  parallel  inclined  planes  and  held  the  same  distance  apart 
throughout  their  length  by  irou  separators  between  the  suspender 
clamps,  in  which  case  the  saddles  on  the  towers  would  be  closer  together. 
Still  the  number  of  cables  suspended  on  each  side  can  not  be  made  very 
large  without  increasing  the  dimensions  of  the  towers  and  the  piers 
supporting  them  far  beyond  the  requirements  of  the  roadway  and  sus- 
pended loads. 

The  vertical  arrangement  of  the  cables  (or  a  combination  of  vertical 
and  horizontal  arrangements)  certainly  presents  some  very  decided 
advantages.  It  requires  less  width  at  the  top  of  the  towers,  and  a  large 
part  of  the  stiffening  of  the  bridge  may  be  obtained  by  trussing  the 
cables  in  a  manner  which  will  be  again  referred  to.  Moreover,  with 
this  arrangement  the  towers  can  be  so  constructed  that  new  cables  can 
be  readily  added  to  meet  future  demands  for  increased  traffic  capacity. 
This  method,  however,  is  not  so  simple  as  the  other,  and  with  large 
loads  and  cables  involves  mechanical  difficulties  which  can  be  properly 
dealt  with  only  after  an  extended  investigation  of  the  problem  as  a 
special  case.  In  this  general  investigation  the  Board  consider  it  best 
to  adopt  the  simpler  arrangement,  as  has  been  done  by  the  New  York 
Board.  Whatever  arrangement  is  adopted,  the  Board  are  of  the  opinion 
that  it  would  not  be  found  convenient  to  work  more  than  eight  cables 
together  as  one  cable  system.  For  the  purposes  of  this  investigation,  it 
is  therefore  assumed  that  the  suspension  bridge  of  maximum  span  is 
supported  by  sixteen  21}-inch  cables.  The  following  list  giving  the 
arrangements  employed  in  a  number  of  important  bridges,  may  be  of 
interest  in  this  connection : 

New  York  and  Brooklyn  Bridge,  1,595.5  feet  span,  has  one  15|-mch 
cable  on  each  side. 

Niagara  Bridge,  821.3  feet  span,  two  10-inch  cables,  one  vertically 
over  the  other. 

Wheeling  Bridge,  1,010  feet  span,  two  8-inch  cables,  side  by  side. 
Fairmount  Bridge,  550  feet  span,  seven  cables,  6  side  by  side  and  1 
above. 

Freiberg  Bridge,  Switzerland,  870  feet  span,  three  cables,  2  side  by 
side  and  1  above. 

Dordogne  Bridge,  France,  350  feet  span,  three  cables,  side  by  side. 

Niagara  Bridge,  at  Lewistown,  1,400  feet  span,  had  four  cables  side 
by  side. 

Menai  Bridge,  600  feet  span,  four  chains  in  the  same  vertical  plane. 
Tweed  Bridge,  Berwick,  450  feet  span,  three  chains  in  the  same  ver- 
tical plane. 

Tersing  Bridge,  over  the  Maas,  two  chains,  one  over  the  other, 
Bridge  Yoconilans,  St.  Honorine,  two  chains,  one  over  the  other. 
La  Roche  Bernard  Bridge,  over  the  Yilaine,  050  feet  span,  two  cables, 
side  by  side. 

Lambeth  Bridge,  England,  two  cables,  side  by  side. 

Donau  Bridge,  Pesth,  600  feet  span,  two  chains,  one  over  the  other. 

Moldau  Bridge,  Prague,  four  chains  in  pairs,  over  each  other. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


13 


LOADS. 

The  total  load  supported  by  the  bridge  will  consist  of  two  parts,  viz, 
the  live  load  or  weight  of  the  passing  traffic  and  the  dead  load  or 
weight  of  the  structure.  It  will  be  convenient  to  consider  the  load 
under  these  two  heads. 

1.  Live  load. — In  another  part  of  this  report  the  difference  in  the 
character  of  the  action  of  the  live  load  upon  a  structure  in  stable 
equilibrium  having  a  certain  degree  of  flexibility  from  that  of  its  action 
upon  a  more  rigid  structure  in  unstable  equilibrium  will  receive  due 
consideration.  For  the  present  we  will  only  determine  the  magnitude 
of  the  live  load.  The  live  load  per  linear  foot  of  span  will  be  repre- 
sented by  q. 

The  greatest  static  effect  upon  the  cable  will  be  produced  by  the 
maximum  load;  that  is,  when  the  whole  platform  from  tower  to  tower 
is  covered  with  the  heaviest  possible  railroad  trains. 

A  suspension  railroad  bridge  of  very  long  span  will  as  a  rule  be 
built  only  over  a  wide  river  or  estuary  navigable  by  ocean  craft  and 
therefore  requiring  a  great  height  of  the  bridge  above  the  water.  To 
limit  the  expense  of  the  shore  extensions  the  approaches  must  be 
given  as  steep  a  grade  as  is  admissible  for  a  railroad  bridge.  It  is 
therefore  assumed  that  the  approaches  will  have  a  grade  of  1  per  cent. 

The  weight  of  a  railroad  train  passing  over  the  bridge  need  not  be 
considered  as  any  greater  than  that  which  the  heaviest  freight  loco- 
motive is  capable  of  hauling  up  a  1  per  cent  grade.  From  a  list  pub- 
lished by  the  Baldwin  Locomotive  Works  it  appears  that  exceptionally 
heavy  locomotives  are  built  with  170,000  pounds  on  the  drivers  and  a 
totafweight  of  192,500  pounds.  The  Baldwin  Works  allow  9  tons  for 
each  1,000  pounds  on  the  drivers  as  the  maximum  efficiency  on  a  grade  of 
1  per  cent.  This  extra  heavy  locomotive  can  therefore  pull  up  on  the 
bridge  1,530  tons  including  its  own  weight.  Subtracting  96  tons  for 
the  weight  of  Jhe  locomotive,  we  have  for  the  weight  of  the  train,  1,434 
tons.  This  is  equal  to  41  hopper-bottom  gondola  cars  each  27  feet  2 
inches  long  and  weighing  35  tons.  The  length  of  the  engine  and  ten- 
der being  54  feet,  the  total  length  of  the  train  will  be  1,168  feet,  and 
the  weight  per  linear  foot  of  track  will  be  2,620  pounds,  equal  to  1.31 
tons.  If  we  suppose  all  6  tracks  to  be  loaded  from  end  to  end  with  such 
trains,  the  live  load  per  linear  foot  will  be  15,720  pounds,  equal  to  7.86 
tons. 

Any  such  loading  as  this,  however,  is  so  extremely  improbable  as  to 
be  a  practical  impossibility;  indeed,  at  the  height  above  water  level  at 
which  such  abridge  must  be  carried,  the  transportation  of  passengers, 
and  not  of  freight,  must  be  the  main  consideration.  A  purely  freight 
traffic  would  in  no  conceivable  location  require  six  tracks  over  a  bridge 
of  very  long  span.  Such  a  number  of  tracks  would  only  be  justified  by 
the  location  of  the  bridge  near  a  very  large  city  and  by  a  large  pas- 
senger traffic.  The  trains  passing  over  such  a  bridge  would  undoubt- 
edly be  controlled  on  the  block  system  and  not  more  than  one  train 
on  each  track  would  be  allowed  upon  the  bridge  at  the  same  rime.  If 
the  stiffening  girders  could  do  their  full  duty  the  weights  upon  the 
bridge  would  be  uniformlv  distributed  and  the  live  load  per  linear  foot 

■        3,060,000     n      18,360,000  =      m      a.  ±  . 

would  be  ^  —  X  6  =  — — ^   pounds.  Tbe  distribution,  how- 
ever, is  not  perfectly  uniform,  and  there  are  occasionally  other  causes 
which  produce  an  increase  in  local  stresses.  The  Board  consider  it  best 
to  add  50  per  cent  to  this  estimate  to  cover  these  uncertainties.  In 


14 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


computing  the  cable  strength,  therefore,  the  adopted  value  of  the  live 
load  will  be — 

27,540,000 
g=  L 

The  live  load  assumed  for  the  Niagara  Suspension  Bridge,  which  has 
a  span  of  800  feet,  is  350  tons  in  a  length  of  450  feet  of  single  track, 
which  is  equivalent  to  1,600  pounds  per  linear  foot  of  train,  or  less 
than  1,000  pounds  per  linear  foot  of  the  entire  span,  with  a  factor  of 
safety  of  4.41  in  the  cables  and  4.0  in  the  stiffening  girders.*  The 
bridge,  however,  safely  carries  heavier  trains  in  daily  operation. 

The  largest  existing  railroad  bridge  is  the  Forth  bridge,  in  Scotland. 
It  has  2  tracks  and  2  spans  of  1,700  feet  each.  It  was  tested  with  2 
heavy  trains  side  by  side,  each  1,000  feet  long  and  weighing  900  tons. 
Each  train  was  drawn  by  2  locomotives  each  weighing  72  tons.  This 
load  was  equivalent  to  1,800  pounds  per  linear  foot  of  track,  or  3,000 
pounds  per  linear  foot  of  span.  These  were  considered  extra  heavy 
train  loads,  very  seldom  occurring  in  actual  operation  on  English  roads.t 

Making  allowance  for  the  heavier  train  loads  of  American  railroads, 
it  will  be  seen  that  3,000  pounds  per  linear  foot  of  track  for  a  length  of 
1,500  feet,  considered  as  distributed  over  the  bridge  from  tower  to 
tower  (which  is  the  value  given  by  our  formula),  is  an  exceedingly  safe 
assumption  of  the  live  load  for  a  very  long  bridge  in  which  the  span 
exceeds  the  length  of  the  maximum  train.  This  value  agrees  very 
nearly  with  that  assumed  by  the  New  York  Board  in  its  estimate  for  a 
u lighter  structure." 

It  is  very  evident  that  the  assumed  live  load  per  unit  of  track  ought 
*  to  diminish  with  the  number  of  tracks  and  with  the  length  of  span.  A 
single-track  bridge  of  short  span  is  strained  nearly  to  its  maximum 
every  time  a  train  goes  over  it.  A  6-track  bridge  is  strained  to  its 
maximum  only  when  6  maximum  trains  are  abreast  of  each  other;  and 
when  the  span  exceeds  the  maximum  train  length  the  maximum  stress 
ought  never  to  occur. 

2.  Bead  load. — This  produces  at  all  times  constant  strains  in  the 
members  of  the  bridge.  It  is  composed  of  the  weights  of  the  following 
parts:  The  suspension  cables  with  their  wrapping,  the  platform,  the 
stiffening  girders,  the  wind  and  sway  bracing,  and  the  suspenders. 
The  weights  of  these  parts  per  linear  foot  of  span  will  be  represented 
as  follows :  Cables  =  w ;  cable  wrapping  =  w0 ;  platform  =pY .;  girders  = 
p2;  bracing  =  p3;  suspenders  =p4. 

(1)  WeU/ht  of  the  suspension  cables. — The  weight  of  a  cable  formed  of 
6,000  parallel  steel  wires,  No.  3,  B.  W.  Gr.,  having  a  diameter  of  21^ 
inches,  without  wrapping,  will  be  1,075  pounds,  or  0.538  tons  per  run- 
ning foot.  If  we  assume  16  cables  for  the  support  of  the  entire  bridge, 
the  total  cable  weight  per  linear  foot  will  be  w'  =  17,200  pounds  = 
8.6  tons;  and  w  =  17,917  =  8.959  tons. 

(2)  Cable  tvrapping. — The  cable  will  be  wrapped  with  iron  wire  of 
No.  9,  B.  W.  Gr.  The  weight  of  this  wrapping  will  be  26  pounds  per 
linear  foot,  and  for  16  cables,  416  pounds.  The  weight  of  wrapping  per 
linear  foot  of  span  will  therefore  be  tc0  =  433  pounds. 

It  will  be  found  convenient  for  the  purposes  of  this  investigation  to 
know  the  relation  between  the  weight  of  the  cable  per  linear  foot  of 
horizontal  span  (w)  and  its  weight  per  foot  measured  in  the  direction 


*  Proceedings  Am.  Soc.  C.  E.,  Vol.  x,  p.  195. 
t  Record  of  the  Forth  Bridge,  p.  64. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


15 


of  its  axis  (wf).  The  cable  curve  will  be  approximately  a  parabola, 
and  its  approximate  length  will  be  fl  +  -jgp  J  L,in  which  L  is  the  hori- 
zontal span  in  feet  and  R  is  the  ratio  of  theversine  of  the  cable  to  the 
span.    Hence  w  =  ^1  wf.    For  reasons  which  will  be  given 

in  the  sequel  the  value  of  R  will  be  assumed  as  8  in  this  investi- 
gation.   For  this  value  we  have  w  =  1.0417  w'  and  ic'  =  0.900  w. 

(3)  Weight  of  the  platform. — In  the  arrangement  adopted  in  tins 
investigation  for  the  purposes  of  estimate  the  cross-girders  sustain  the 
weight  not  only  of  the  live  load  but  also  of  the  stiffening  girders  and 
lateral  bracing.    The  distance  between  the  cross-girders  is  30  feet. 

The  platform  further  consists  of  longitudinal  girders  (stringers),  the 
permanent  way  consisting  of  ties  and  rails  and  the  covering.  Its  con- 
struction is  the  same  as  in  any  other  railroad  bridge. 

The  weights  of  the  stiffening  girders  and  lateral  bracing  (which 
increase  with  the  span),  are  imposed  upon  the  cross-girders  so  very 
near  the  points  of  suspension  that  the  weight  of  the  platform  may  be 
considered  practically  independent  of  the  span.  The  weight  per  linear 
foot  of  span  for  a  6-track  platform,  carrying  stiffening  girders  and  brac- 
ing, for  a  span  of  3,200  feet,  was  determined  by  the  New  York  Board 
to  be  7,200  pounds.  We  may  therefore  adopt  in  this  investigation  the 
constant  value  ^  =  7,200  pounds=3.6  tons. 

(4)  Weight  of  the  stiffening  girders. — It  will  be  shown  under  the  head 
of  Vertical  Bracing  that  the  weight  of  the  two  stiffening  girders  per 
linear  foot  of  6-track  bridge  may  be  found  in  pounds  from  the  for- 
mula p,=  3,281+  2.754  L  +  0.0005312  L2.  This  includes  an  allowance  of 
material  in  the  lower  chords  to  provide  for  the  stresses  due  to  wind. 

(5)  Weight  of  the  lateral  bracing. — As  will  be  shown  under  the  head 
of  Lateral  Bracing,  the  weight  of  the  wind  and  sway  bracing  per 
linear  foot  of  6-track  bridge  (so  far  as  not  provided  for  in  the  preceding 
paragraph)  will  be  given  in  pounds  by  the  formula  p3=  2,420  -f 
0.3889  L.  ? 

(6)  Weight  of  the  suspenders. — The  suspended  load  is  connected  with 
the  cables  by  8  wire  suspenders  on  each  side  of  the  bridge  at  each 
cross-girder.  The  suspenders  at  each  girder  are  equal  in  length  and 
are  supposed  to  be  adjusted  so  as  to  carry  practically  equal  portions  of 
the  load.    At  the  middle  of  the  span  the  cables  are  60  feet  above  the 

level  of  the  suspension  pins.    The  versine  of  the  cable  being  ^  the 

average  length  of  a  suspender  is  ^  +  60.    Assuming  a  unit  working 

stress  of  30,000  pounds  and  adding  20  per  cent  for  constructive  details, 
the  weight  of  the  suspenders  per  linear  foot  of  span  will  be 

*<  =  tbSrf  (h  +  60)  ^-».) 

in  which  p'  =  q  +  Pl  +  p2  +  p3  +  p4  +  w0. 

For  the  purposes  of  this  computation  we  may  assume  p4  =  1,300  in 
the  value  of  p'  —  ica. 

From  values  previously  given  we  find  p' — wo=14200-f-27540000  L  1 
+  3.1429  L+0.0005312   L2;   and  i>4=272+224726  L  ^O.IOOIO  L  + 
0.00002215  L2+ 0.000000003  L3. 
S.  Ex.  1  7 


16 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


(7)  Total  suspended  iceight. — The  total  suspended  weight  per  linear 
foot  of  span  exclusive  of  the  cables  will  be  p' =q+pi+p2+p-i-\-Pt+ w0= 
13605  +  27764726  ^+3.24906  L  +  0.00055335  L2+  0.000000003  L3. 

WIND  PRESSURES. 

The  wind  pressure  upon  a  large  bridge  is  of  such  magnitude  as  to 
require  especial  consideration.  In  the  principal  members  of  the  Forth 
bridge  (a  cantilever  construction),  the  maximum  stresses  due  to  wind 
have  been  stated  by  its  engineer  to  be  more  than  one-quarter  greater 
than  those  due  to  the  dead  weight  of  the  bridge  and  nearly  three 
times  as  great  as  those  due  to  the  live  load  of  passing  trains.  In  sus- 
pension bridges  these  wind  stresses,  though  they  may  be  less  than  in 
other  bridges,  are  still  of  very  great  importance,  and  must  be  carefully 
provided  against  by  the  introduction  of  metal  which,  while  adding 
nothing  to  the  carrying  capacity  of  the  bridge,  does  add  considerably 
to  its  dead  load,  and  therefore  necessitates  an  increase  in  the  strength 
of  suspenders,  main  cables,  towers,  anchorages  and  foundations,  and 
thus  may  add  enormously  to  the  total  cost  of  the  bridge.  Under  such 
circumstances,  while  it  is,  on  the  one  hand,  important  to  secure  a  suffi- 
ciency of  wind  bracing,  it  is,  on  the  other  hand,  equally  important  not 
to  use  any  more  than  is  actually  necessary. 

Since  the  existing  fund  of  information  as  to  wind  pressures,  as  to 
their  effect  on  bridges,  and  as  to  the  present  most  used  methods  of 
dimensioning  wind  bracing,  is  either  quite  limited  or  else  is  not  easily 
accessible,  it  has  been  thought  well  to  attach  hereto  a  full  history  of 
past  work  in  this  direction  with  suggestions  of  rules  for  use  in  the 
dimensioning  of  large  structures  in  places  exposed  to  heavy  winds. 
(See  Appendix  0.) 

Past  history  shows  the  possibility,  at  almost  any  place,  of  an  occa- 
sional tornado  of  power  sufficient  to  destroy  almost  any  existing  engineer- 
ing structure.  Such  tornadoes,  like  violent  earthquakes,  are  so  rare  that 
no  large  constructions  of  to-day  are  made  thoroughly  proof  against  them. 
In  such  a  tornado,  however,  a  suspension  bridge  would  fare  much  bet- 
ter than  any  other  form  of  bridge,  as  it  offers  the  least  surface  to  the 
wind,  as  its  overturning  is  almost  a  physical  impossibility,  and  espe- 
cially as  the  loss  of  large  parts  of  its  roadway  and  stiffening  trusses 
would  not  necessarily  destroy  its  main  cables  and  towers  (these  being 
its  essential  and  costly  features).  The  Board  have  therefore  (for  rea- 
sons stated  in  the  Appendix)  considered  a  maximum  steady  wind 
pressure  of  30  pounds  per  square  foot  over  the  entire  structure  and 
over  a  continuous  train,  reaching  entirely  across  the  bridge,  and  also  a 
similar  30-pound  pressure  over  the  unloaded  bridge,  accompanied  by 
an  added  pressure  of  20  pounds  per  square  foot  (making  50  pounds  in 
all)  over  1,000  feet  of  the  unloaded  bridge;  this  latter  allowance  being 
made  to  provide  for  occasional  severe  gusts. 

The  exposed  surface  of  the  bridge  and  load  per  running  root  (by  the 
method  of  calculation  given  in  full  in  the  Appendix)  is  taken  at  30 
square  feet  for  the  cables  and  suspenders,  49  square  feet  for  the  stiffen 
ing  girder  (including  the  upper  chord,  lower  chord,  web  members, 
horizontal  diagonals,  and  sway  bracing),  18  square  feet  for  the  plat- 
form (including  track,  guard  rails,  ties,  cross-girders,  and  stringers), 
and  8  square  feet  for  the  train  (excluding  the  portion  sheltered  by  the 
high  bottom  chords  and  other  adjacent  parts  of  the  stiffening  girders). 
In  view  of  th£  heavy  weights  and  consequent  great  inertia  of  the  cables 
and  stiffening  girders,  the  resulting  wind  pressure  is  treated  as  uni- 
formly distributed  over  the  entire  bridge  from  end  to  end;  chough  a 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


17 


more  careful  distribution,  perhaps  saving  considerable  metal,  would  be 
adopted  in  actual  practice. 

The  cradling  of  the  main  cables  and  suspenders  is  considered  suffi- 
cient to  amply  resist  the  1.050  pounds  per  square  foot  of  wind  pressure 
due  to  the  30  square  feet  per  linear  foot  of  their  own  surfaces. 

The  wind  bracing  of  the  stiffening  truss  will  then  have  to  resist  only 
the  wind  pressure  on  the  stiffening  truss,  platform,  and  train;  which 
amounts  to  2,345  pounds  per  linear  foot  for  the  unloaded  bridge,  and 
2,250  pounds  per  foot  for  the  loaded  bridge. 

As  the  stiffening  truss  is  hinged  at  its  middle,  the  wind  bracing  (at 
least  near  the  ends  of  the  half  trusses)  must  be  arranged  to»carry  all 
the  wind  stresses  to  the  bottom  chord;  so  that  this  bracing  is  taken  as 
composed  of  a  very  light  upper  horizontal  truss  (not  theoretically 
necessary),  of  a  strong  vertical  sway  bracing,  and  of  a  heavier  lower 
horizontal  truss.  Since  the  wind  trussing  may  be  combined  with  the 
adjacent  parts  of  the  stiffening  girder  and  platform,  this  lower  wind 
truss  will  be  built  up  by  increasing,  where  necessary,  the  dimensions 
of  the  cross  girders  of  the  platform,  and  the  lower  chords  of  the  stiffen- 
ing truss,  and  by  inserting  cross  diagonals  between  them. 

Because  of  the  great  size  of  these  cross  girders  and  lower  chords, 
and  therefore  the  great  excess  of  strength  in  this  lower  truss  when  the 
bridge  is  unloaded,  the  Board  regard  the  2,250  pounds  per  linear  foot 
of  wind  pressure  on  the  loaded  bridge  as  the  one  which  throws  the 
greatest  strain  upon  its  members,  and  therefore  take  this  value  as  the 
one  to  be  used  in  combination  with  the  other  loads  upon  a  bridge  of 
maximum  length. 

In  case  further  lateral  stiffness  against  wind  should,  at  any  time,  be 
thought  desirable,  it  may  be  obtained  by  the  use  of  horizontal  wind 
cables  under  the  platform;  and  small  main  cables  may  at  any  time  be 
added,  if  found  necessary,  to  support  the  added  weight  of  such  wind 
cables;  but  the  Board  consider  the  use  of  such  wind  cables  unnec- 
essary. # 

OSCILLATIONS. 

In  considering  the  character  and  importance  of  small  motions  in 
bridges  it  is  necessary  to  distinguish  carefully  between  stability  and 
rigidity.  A  suspension  bridge  is  the  most  stable  of  all  bridge  struc- 
tures. The  locus  of  the  centers  of  gravity  of  its  vertical  cross-sections 
lies  far  below  the  points  of  support.  The  live  load,  which  is  the  main 
cause  of  its  vertical  oscillations,  always  moves  below  the  gravity-line, 
thereby  increasing  the  lateral  stability  of  the  structure.  As  the  span 
is  increased  the  gravity-line  rises,  but  the  resulting  slight  decrease  in 
stability  is  more  than  compensated  for  by  the  diminution  in  the  ratio  of 
the  live  to  the  permanent  load.  The  small  motions  of  erect-arch  and 
deck  bridges  must  be  carefully  conlined  within  small  limits  to  insure  the 
safety  of  the  structures,  but  there  is  no  such  necessity  in  the  case  of 
suspension  bridges,  where  the  system  is  in  stable  equilibrium  and  sure 
to  return  to  its  position  of  rest  whatever  may  be  the  magnitude  of  the 
displacement. 

The  lateral  oscillations  are  due  mainly  to  the  action  of  the  wind. 
These  are  met  not  only  by  the  great  weight  of  the  structure,  but  also  by 
the  cradling  of  the  cables,  which  much  increases  the  lateral  stability. 

It  is  possible  to  construct  a  suspension  bridge  so  that  it  will  have 
any  degree  of  rigidity  desired,  but  it  will  appear  from  the  above  that 
rigidity  is  in  this  case  of  much  less  importance  than  it  is  in  most  other 
kinds  of  bridges;  indeed,  it  may  be  shown  that  a  certain  small  flexi- 
bility is  a  positive  advantage  in  suspension  bridges. 

S.  Ex.  12  2 


18 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  Board  do  not  consider  it  necessary  to  give  in  this  report  an 
elaborate  development  of  the  theory  of  bridge  oscillations,  because  it 
is  perfectly  easy  to  stiffen  a  suspension  bridge  so  as  to  reduce  both  its 
vertical  and  lateral  deflections,  and  consequently  the  duration  of  its 
oscillations,  within  any  desired  limits;  and  in  bridges  of  very  long- 
span,  where  the  ratio  of  live  to  dead  load  is  comparatively  small,  no 
difficulty  from  this  cause  need  be  anticipated.  The  following  brief 
remarks  on  this  subject  relate  to  suspension  bridges  of  comparatively 
small  weight  and  span. 

As  before  remarked,  oscillations  in  suspension  bridges  are  mainly 
produced  by  the  impulses  of  the  moving  load  and  by  the  pressure  of 
the  wind.  The  magnitude  of  the  oscillations  is  sometimes  increased  by 
the  lengthening  of  the  central  part  of  the  cable,  due  to  the  straighten- 
ing of  the  chains  of  the  side  span  under  the  action  of  a  load  on  the  cen- 
tral span.  Theoretically  an  infinitely  small  impulsive  force  may  produce 
an  infinitely  small  amplitude  of  oscillation  of  finite  duration.  If  such 
impulses  are  repeated  a  summation  of  their  effects  may  result.  This 
will  occur  when  the  interval  between  two  impulses  is  equal  to  the  time 
of  oscillation,  and  may  occur  when  it  is  greater.  Under  these  circum- 
stances small  impulsive  forces,  by  many  repetitions,  may  produce  a 
great  oscillation  in  an  elastic  or  suspended  body.  In  this  way  the  wind 
has  been  known  to  raise  waves  in  the  platform  of  a  light  suspension 
bridge. 

In  the  case  of  a  bridge  truss  it  is  important  that  the  time  of  oscilla- 
tion produced  by  a  load  acting  impulsively  should  not  exceed  a  certain 
amount,  in  order  that  the  oscillations  may  not  be  cumulative. 

In  highway  bridges  it  is  especially  the  measured  step  of  pedestrians 
which  gradually  augments  the  amplitude  of  the  oscillation  when  the  time 
of  oscillation  is  equal  to  or  greater  than  the  time  of  a  step,  which  may 
be  assumed  as  from  0.6*  to  0.7  second.  If  the  time  of  oscillation  of  the 
structure  is  greater,  it  can  adjust  itself  to  the  time  of  a  step  by  the  for- 
mation of  centers  of  oscillation.  The  result  is  that  by  the  gradual 
accumulation  of  energy  changes  of  form  are  produced  which  are  con- 
siderably greater  than  those  produced  by  an  equivalent  static  load. 

These  oscillations  occur  not  only  in  elastic  or  stiffened  systems,  bu* 
also  in  slack  systems.  A  freely  suspended  heavy  chain  moved  from 
the  position  of  equilibrium  in  its  vertical  plane  will  assume  oscillating 
motions  which  will  gradually  increase  if  new  impulses  occur  in  the 
time  intervals  corresponding  to  the  time  of  oscillation  or  a  fraction 
thereof.  It  is  shown  by  Melan  that  the  time  of  oscillation  of  a  slack 
chain  is  materially  greater  than  that  of  even  a  very  elastic  construc- 
tion, which  explains  the  well-known  fact  that  unstiffened  suspension 
bridges  can  very  easily  be  brought  into  great  oscillations  by  a  few 
pedestrians. 

Prof.  Melan  in  his  treatise  on  Bridge  Construction  deduces  the  equa- 
tions t  =  1.806  \// and  t=  2.0063  \/  u  +  0.8  for  the  times  of  oscilla- 
tion in  a  slack  and  a  stiffened  system,  respectively;  in  which  t  is  the 
time  of  oscillation  in  seconds,  /is  the  versine  of  the  cable  in  meters, 
u0  is  the  deflection  in  the  middle  due  to  the  uniformly  distributed  dead 
load,  and  u  is  the  increase  of  deflection  due  to  a  concentrated  load  in 
the  position  of.  rest  in  meters. 

From  these  formulas  it  follows  that  the  time  of  oscillation  of  a  bridge 
structure  depends  only  upon  the  magnitude  of  its  deflection  in  the 
position  of  rest,  no  matter  what  may  be  the  character  or  size  of  the 
structure.    Hence  the  deflection  must  be  kept  within  certain  limits,  in 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


19 


order  that  the  bridge  may  not  be  set  in  vibration  by  the  steps  of 
pedestrians  or  other  regularly  repeated  impulses. 

The  time  of  oscillation  and  consequently  the  deflection  must  be  the 
smaller  the  more  rapidly  the  repetition  of  impulses  occurs.  Hence 
greater  stiffness  is  required  in  a  railroad  suspension  bridge  than  in  a 
similar  highway  bridge. 

As  the  deflection  u0  due  to  the  uniformly  distributed  load  is  in  general 
proportional  to  the  fourth  power  of  the  span,  it  follows  that  the  time 
of  oscillation  varies  approximately  as  the  square  of  the  span.  There- 
fore, this  time  may  be  diminished  by  fastening  the  structure  at  interme- 
diate points  to  the  shore  or  ground  so  as  to  form  a  number  of  centers 
of  oscillation. 

The  occurrence  of  cumulative  oscillations  may  also  be  prevented  by 
employing  together  several  systems  for  stiffening  the  cables,  these  sys- 
tems having  different  periods  of  oscillation;  and  where  a  number  of 
cables  are  assembled  on  each  side  of  the  bridge,  the  same  result  may 
be  accomplished  by  employing  different  versines  for  the  cable  curves. 
Thus,  in  the  bridge  designed  by  Mr.  Gustav  Lindenthal  for  the  North 
River  Bridge  Company,  the  stiffening  is  obtained  by  trussing  between 
the  cables  and  by  continuous  longitudinal  platform  girders.  As  these 
two  systems  have  different  periods  the  chance  of  cumulative  oscilla- 
tions is  greatly  reduced.  In  the  Niagara  Suspension  Bridge  the  two 
systems  of  cables  have  versines  of  54  and  64  feet,  respectively,  and 
consequently  different  periods  of  oscillation. 

The  arrangements  to  prevent  deflections  due  to  the  moving  load 
and  the  wind  will  receive  consideration  in  other  parts  of  this  report. 

BRACING. 

The  bracing  required  to  stiffen  the  bridge  may  be  conveniently  con- 
sidered under  two  heads,  vertical  bracing  and  lateral  bracing. 

1.  Vertical  bracing. — It  is  the  object  of  this  bracing  to  confine  within 
definite  and  small  limits  the  oscillations  and  deflections  caused  mainly 
by  the  rolling  load.  Various  methods  have  been  employed  for  this 
purpose,  the  principal  of  which  are  as  follows: 

(1)  Stays  extending  from  the  tops  of  the  towers  to  the  platform. 

(2)  Stays  extending  from  the  bottoms  of  the  towers  to  the  cables. 

(3)  Longitudinal  stiffening  girders  connected  with  the  platform  and 
extending  over  the  whole  length  of  the  bridge. 

(4)  Bracing  between  two  cables  hanging  in  the  same  vertical  plane. 

(5)  Trussing  the  cable  on  its  concave  side. 

(6)  Trussing  between  the  cable  and  the  platform. 

Two  or  more  of  these  methods  of  stiffening  are  frequently  ejnployed 
together  in  the  same  bridge.  For  example:  Methods  (1)  and  (3)  are 
employed  at  the  East  River  Bridge;  method  (3)  at  the  Niagara  Bridge; 
method  (4)  at  the  Allegheny  River  Bridge  at  Seventh  street,  Pitts- 
burg; method  (5)  at  the  Point  Bridge  over  the  Monongahela  at 
Pittsburg;  method  (6)  at  the  Lambeth  Bridge,  England.  Experience 
has  proved  all  these  methods  to  be  effective,  and  for  some  of  them 
special  advantages  of  economy  are  claimed.  Thus  the  over-floor  stays 
of  method  (1)  not  only  prevent  the  development  of  large  vertical 
oscillations  in  the  platform,  but  also  relieve  the  suspension  cables  of  a 
considerable  part  of  the  load.  In  method  (2)  the  stays  add  to  the 
weight  on  the  cables  instead  of  relieving  them,  and  in  this  respect  it  is 
not  as  good  as  method  (1).    It  has  been  objected,  however,  to  the  use 


20 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


of  stays  in  bridges  of  large  span  that  they  complicate  the  conditions 
of  equilibrium,  as  it  is  difficult  to  adjust  them  so  as  to  bear  a  definite 
portion  of  the  stresses  under  the  varying  conditions  of  load  and 
temperature.  By  bracing  two  cables — method  (4) — we  utilize  the  cables 
as  the  chords  of  the  stiffening  girder  and  save  the  material  otherwise 
required  for  the  chords.  Still  greater  economy  is  claimed  for  combina- 
tions of  the  stiffening  systems. 

The  simplest  and  most  employed  stiffening  system  is  the  longitudi- 
nal stiffening  girder.  Such  girders  are  convenient  for  supports  to  the 
lateral  bracing  and  for  side  guards,  and  at  none  of  the  existing  bridges 
where  other  methods  were  employed  was  the  girder  entirely  dispensed 
with  as  a  part  of  the  stiffening  system.  The  girder  rests  upon  the 
floor  beams  and  is  thus  suspended  from  the  cable.  It  does  not  support 
any  load,  but  merely  distributes  it,  hence  it  is  absolutely  a  dead  weight, 
adding  nothing  to  the  strength  of  the  bridge. 

The  Board  consider  it  very  probable  that  for  a  given  special  case  a 
lighter  and  better  stiffening  system  than  that  supplied  by  the  simple 
longitudinal  platform  girder  could  be  worked  out  by  combining  the 
trussed  cables  and  longitudinal  girder  systems,  as  has  been  done  by 
Mr.  Gustav  Lindenthal  in  his  elegant  design  for  the  North  Biver 
Bridge.  In  applying  this  method,  however,  to  wire  cables  carrying 
very  heavy  weights  over  a  very  long  span  some  new  questions  of  con- 
structive detail  will  require  solution,  and  for  the  purposes  of  a  general 
investigation  it  seems  best  to  follow  the  usual  method  of  stiffening.  It 
will,  therefore,  be  assumed  that  vertical  stiffness  is  obtained  entirely 
by  longitudinal  platform  girders  with  parallel  chords. 

These  girders  are  usually  of  the  open  frame  or  lattice  type.  While 
their  rigidity  does  not  affect  the  actual  safety  of  the  cables  which 
carry  the  entire  dead  and  live  load,  it  does  determine  the  suitability  of 
the  bridge  for  railroad  purposes.  There  is  no  doubt  that  a  suspension 
bridge  can  be  made  as  rigid  for  railroad  trains  as  a  bridge  of  any  other 
system. 

If  a  flexible  cable  be  loaded  ununiformly  it  will  be  depressed  on  the 
side  of  the  heaviest  load  and  will  rise  on  the  opposite  side.  It  is  the 
object  of  the  stiffening  girder  to  reduce  the  distortion  of  the  cable  to  a 
practical  minimum.  There  are  two  practical  ways  in  which  the  girder 
may  be  constructed: 

(1)  As  a  continuous  girder,  loosely  supported  at  the  ends  with  reac- 
tions in  both  vertical  directions,  but  permitting  horizontal  motion. 

(2)  As  a  girder  loosely  supported  at  the  ends,  as  in  the  first  case, 
and  hinged  in  the  middle. 

For  the  first  case  the  problem  of  equilibrium  is  statically  inde- 
terminate; that  is,  the  conditions  of  equilibrium  can  not  be  formulated 
without  including  the  elastic  forces  developed  in  the  girder.  In  the 
second  case  we  have  only  to  deal  with  static  forces,  and  the  stresses  in 
the  girder  can  be  calculated  with  a  close  degree  of  approximation  by 
the  simple  law  of  the  lever. 

In  the  designing  of  stiffening  girders  the  formulas  given  by  Prof. 
Kankine  have  generally  been  employed.  The  formulas  for  the  continu- 
ous girder  are  deduced  in  his  Applied  Mechanics  (p.  370).  The 
formulas  for  the  hinged  girdei  are  given,  but  not  deduced,  in  his  Civil 
Engineering  (x>.  579).  Bankine's  methods,  which  are  approximate  in 
character,  have  been  extended  to  a  high  degree  of  accuracy  by  subse- 
quent investigators.  Probably  the  most  complete  investigation  of  the 
straight  stiffening  girder  is  that  of  Prof.  J.  Melan,  of  the  Technical 
High  School  at  Briinn. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


21 


Rankine's  values  of  tlie  maximum  bending-  moments  for  the  hinged 
and  continuous  girders  are  as  follows:  Hinged  girder,  M=0.0156r/L2; 
continuous  girder,  M=0.017SbV/L2;  while  Melan,  by  more  accurate 
methods,  obtains  for  the  hinged  girder  M=0.018S3f/L2,  and  for  the 
continuous  girder  M=0,01652gIA  It  will  be  noticed  that  with  Ran- 
kine's  values  the  maximum  bending  moment  is  smaller  for  the  hinged 
girder  than  for  the  continuous  girder,  while  with  Melan's  values  the 
reverse  is  the  case. 

Although  the  hinged  girder  presents  very  decided  theoretical  advan- 
tages, especially  in  the  determination  of  the  stresses,  it  has  some  dis- 
advantages which  have  prevented  its  employment  in  any  important 
practical  case.  The  introduction  of  the  middle  joint  lias  for  its  princi- 
pal object  the  attainment  of  a  static  determination,  but,  as  Melan  has 
pointed  out,  the  theoretical  conditions  can  not  be  fully  satisfied  unless 
the  girder  and  cable  have  a  common  joint  at  the  middle.  If  the  girder 
alone  is  jointed,  increased  bending  strains  must  be  produced  in  the  cable 
directly  over  the  joint.  The  arrangement  of  the  wind-bracing  becomes 
more  troublesome,  for,  since  the  upper  chords  of  the  girders  are  cut, 
all  the  wind  stresses  must  be  transferred  to  the  lower  chords.  The 
wind-bracing  would  doubtless  be  heavier  than  for  a  continuous  girder. 

Mr.  Lindenthal  has  shown  that  while  there  are  no  temperature 
stresses  in  a  three-hinged  arch  at  the  middle  hinge  they  do  exist  for 
any  change  from  the  normal  temperature  in  the  connected  half-arches. 
His  investigation  of  this  important  question  (which  originally  appeared 
in  the  Engineering  News  of  March  10,  1888,  and  which  has  been  revised 
by  him  for  the  Board)  will  be  found  in  Appendix  D.  For  the  purposes 
of  this  investigation,  however,  there  is  no  question  that  the  hinged 
girder  ought  to  be  adopted,  in  order  to  avoid  the  complicated  formulas 
which  would  be  required  in  the  other  case.  It  will  give  results  as 
accurate  as  the  nature  of  the  inquiry  permits  and  on  the  safe  side  as 
regards  weight  of  metal,  which  could  be  considerably  reduced  for 
any  given  casein  practice  by  the  use  of  continuous  girders,  or  by  other 
methods  requiring  more  extended  computations.  The  New  York  Hoard 
employed  the  same  method. 

It  will  appear  hereafter  that  when  considerable  rigidity  is  required, 
as  in  railroad  bridges,  the  stiffening  truss  becomes  the  greatest  single 
element  of  weight  and  therefore  its  economical  designing  is  a  matter  of 
the  highest  importance.  The  Board  therefore  appends  to  this  report  a 
translation  of  Prof.  Melan  s  complete  investigation  of  the  straight  stif- 
fening girder,  which  it  is  believed  is  unknown  to  most  American  bridge 
engineers.  A  simpler  investigation,  but  sufficiently  rigorous  for  all 
practical  purposes,  covering  both  the  hinged  and  continuous  girders, 
has  been  attached  by  the  New  York  Board  as  an  appendix  to  its  report. 

In  the  case  of  the  hinged  girder  the  greatest  distortion  of  the  cable 
occurs  when  the  moving  load  covers  the  platform  from  one  tower  to  a 
point  at  a  distance  0.105  L  from  the  middle  of  the  bridge.  It  is  here 
assumed  that  there  will  be  practically  no  temperature  strains  and  the 
simple  statical  conditions  will  enable  us  to  express  with  sufficient 
accuracy  the  weight  of  the  girder  in  terms  of  the  span. 

The  values  of  tlie  bending  moments  and  shears  which  will  be  used 
in  determining  the  weight  of  the  girder  are  based  upon  the  following 
assumptions: 

1.  The  stiffening  girders  are  supposed  to  have  a  height  sufficient  to 
prevent  great  vertical  flexure.  So  far  as  the  vertical  strains  due  to 
loading  are  concerned  it  is  most  economical  to  make  the  height  as  great 
as  is  practically  possible,  and  with  the  hinged  girder  this  may  be  done, 


22 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


since  changes  of  temperature  are  without  material  influence.  The 
height  of  the  girder  will  therefore  be  assumed  at  120  feet,  as  adopted 
by  the  New  York  Board. 

2.  The  tensions  on  the  suspenders  are  supposed  to  be  always  equal; 
that  is,  the  vertical  reaction  between  the  cable  and  the  girder  is  uni- 
formly distributed  over  the  whole  length  of  the  span ;  and  the  tensions 
on  the  cable  are  assumed  to  be  invariable.  It  has  been  shown  by  M. 
Boulongne*  that  in  the  case  of  the  suspenders  the  values  obtained  on 
this  hypothesis  can  not  be  in  error  more  than  5  per  cent,  and  for  the 
cables  the  error  is  on  the  safe  side,  since  it  increases  the  amount  of 
work  required  of  the  girder. 

3.  The  effects  of  the  elastic  elongation  of  the  suspenders,  due  to  live 
load  and  temperature  changes,  are  neglected.  As  remarked  by  the 
New  York  Board,  these  disturbances  can  be  avoided  by  omitting  the 
suspenders  for  a  short  distance  next  the  towers. 

The  discussion  of  the  values  of  the  maximum  bending  moments  and 
shears  is  omitted  from  this  report,  as  it  is  given  fully  in  Melan's  investi- 
gation (Appendix  E),  and  also  in  Appendix  E  to  the  report  of  the  New 
York  Board. 

The  curve  of  maximum  bending  moments  covering  the  half  girder, 
whose  length  is  ^  L,  is  very  nearly  a  parabola,  and  its  area  is  very  nearly 

§  X  i>  X  0.01883  q  It2.  The  average  maximum  bending  moment  will  there- 
fore be 

Mm=0.01255  q,  L2. 

The  average  maximum  chord-stress  is  found  by  dividing  this  moment 
by  the  height  of  the  girder;  the  area  of  the  cross-section  of  the  chord 
in  square  indies  is  obtained  by  dividing  this  chord  stress  by  the 
assumed  working  unit  stress;  and  the  theoretical  weight  of  the  chord 
per  linear  foot  by  multiplying  this  area  by  3.4  pounds.  To  obtain  the 
practical  weight  the  theoretical  weight  must  be  increased  by  about  25 
per  cent  for  constructive  details.  Although  the  chords  are  subject  to 
reversal  of  strains,  the  Board  have  assumed  a  unit  working  stress  of 
15,000  pounds,  for  reasons  which  will  be  fully  explained  elsewhere. 

The  weight  of  the  upper  chord  in  pounds  per  linear  foot  will  there- 
fore be — 

0M25%^^ ^000000008968  «,  LV 

The  dimensions  of  the  lower  chord  will  have  to  be  considerably 
increased,  as  it  serves  also  as  a  chord  in  the  wind  girder.  Assuming 
for  computation  a  wind  pressure  of  2,250  pounds  per  linear  foot,  for 
reasons  before  given,  the  average  maximum  bending  moment  due  to 
the  wind  will  be — 

Mmw=187.5  L2 

The  unio  working  stress  will  be  assumed  at  30,000  pounds  per  square 
inch  for  reasons  which  will  be  given  elsewhere.  Kemembering  that 
the  width  of  the  track-platform  between  the  axes  of  the  girders  is  100 
feet,  we  obtain  for  the  weight  per  linear  foot  of  materia)  to  be  added 
to  the  lower  chord  to  take  care  of  the  wind-stresses 

187.5  Lx3.4xl.25=0  0002656  u 
30,000x100 


*  Note  sur  les  Pouts  Suspendus,  Amiales  des  Ponts  et  Chaussees,  7  Serie.  Tome  1, 
1892,  p.  742. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


23 


The  average  total  weight  per  linear  foot  of  the  lower  chord  is  there- 
fore 

(0.0002656+0.00000002963  qx)  L2 

The  shearing  stresses  due  to  a  continuous  moving  load  are  greatest 
at  the  origin  of  the  span  and  diminish  to  0,  changing  from  upward  to 

downward  stresses  at  a  distance  ^  from  the  origin.  The  average  max- 
imum shear  without  regard  to  sign  for  all  positions  from  the  origin  to 
the  middle  pin  is  S= 0.1038  qjj. 

The  theoretical  weight  of  the  web  must  be  increased  by  about  50  per 
cent  for  constructive  details  and  to  provide  for  the  transfer  of  weight 
from  the  upper  to  the  lower  chord.  The  lattice  bars  being  placed  at 
an  angle  of  45°,  the  weight  of  the  web  per  linear  foot  of  span  will  be 

0J0381jLL^4Lxl.5><2  =0  00007058  qJj 
15,000 

For  the  total  weight  per  linear  foot  of  each  stiffening  girder  we 
finally  obtain  by  addition 

P^=qi  (0.00007058  L+ 0.00000005926  L2)  +  0.0002650  L2. 

The  value  of  qi9  which  is  to  be  employed  in  this  formula,  must  now 
be  determined.  It  will  be  remembered  that  the  stiffening  girders 
carry  no  weight,  not  even  their  own.  They  simply  distribute  the 
inequalities  of  the  live  load  and  limit  the  deflections  in  the  cables  and 
floor  system.  The  girders  must  be  dimensioned  with  special  reference 
to  those  positions  of  the  live  load  which  correspond  to  the  greatest 
deflection.  The  maximum  bending  moment  in  either  half- girder 
corresponds  to  a  continuous  live  load  extending  from  the  origin 
towards  the  middle  of  the  span  and  covering  a  distance  0.395  L.  For 
all  spans  up  to#2,957  feet  (equal  to  the  maximum  train  length  divided 
by  0.395),  the  single  freight  train  on  each  track  (all  six  trains  being 
supposed  to  advance  together  with  their  engines  abreast)  will  produce 
the  maximum  bending  effects,  the  length  of  such  a  train  being  1,168 
feet.  For  greater  spans  it  is  evident  that  the  maximum  effect  will  not 
be  thus  produced.  Accordingly,  for  spans  greater  than  2,957  feet  we 
should  divide  the  maximum  train  load  by  0.395  L  to  obtain  the  live 
load  per  linear  foot  of  span  to  be  used  in  determining  the  weight  of  the 
stiffening  girders. 

The  weight  of  the  train  is  3,060,000  pounds ;  hence  for  each  girder 
we  obtain 

_  3060000  x  3  _  23210506 
qi  -    0.395  L    -  L 
and  by  substitution  in  the  preceding  equation 

|2  =  1640.3  +  1.377  L  +  0.0002656  L2 

The  total  girder-load  per  linear  foot  for  the  whole  bridge  will  there- 
fore be  p2  =  3281  +  2.754  L  +  0.0005312  L2. 

This  formula  leaves  entirely  out  of  consideration  the  fact  that  part  of 
the  live  load  is  taken  up  directly  by  the  cables,  yet  it  is  certain  that  a 
considerable  part  of  the  action  of  "the  live  load  may  be  thus  absorbed. 
In  his  reconstruction  of  the  Niagara  Suspension  Bridge,  Mr.  L.  L.  Duck, 
the  engineer  in  charge,  provided  for  a  maximum  deflection  of  15  inches 
in  500  feet,  and  thus  reduced  the  value  of  2q{  in  his  formulas  from  0.8 
ton  to  0.6  ton.    Mr.  W.  Hildenbraud,  in  his  reports  relative  to  a  pro- 


24 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


posed  suspension  bridge  across  the  Hudson  Kiver,  which  are  appended 
to  the  report  of  the  isew  York  Board,  provides  for  a  maximum  deflec- 
tion giving  a  grade  not  exceeding  1  per  cent.  He  thereby  reduces  2q{ 
from  9,000  pounds  to  7,800  pounds.  The  Board  do  not  doubt  that  within 
narrow  limits  a  certain  degree  of  flexibility  is  an  advantage  to  the 
bridge.  Deflections  in  a  system  of  stable  equilibrium  do  not  impair  the 
safety  of  the  structure  as  they  do  in  an  unstable  system  like  the  upright 
arch,  and  they  may  exert  a  very  beneficial  influence  in  modifying  the 
dynamic  effects  of  a  rapidly  varying  live  load.  On  the  other  hand,  it 
is  to  be  remarked  that  any  increase  in  the  grade  of  the  track -platform 
is  accompanied  for  fast  trains  by  a  certain  increase  in  the  dynamic 
action  of  the  live  load. 

The  proportion  of  live  load  absorbed  by  the  cables  increases  as  the 
catenary  becomes  flatter,  but  the  cables  must  be  made  heavier.  It  is 
not  easy  to  determine  satisfactorily  the  resultant  effect  of  these  deflec- 
tions, and  in  order  to  be  on  the  safe  side  the  Board  make  no  allowance 
for  them  in  this  investigation. 

Lateral  bracing. — The  principal  duty  of  the  lateral  or  sway  bracing 
is  to  resist  the  action  of  the  wind.  The  top  lateral  system  is  a  light 
riveted  lattice  connecting  the  top  chords  of  the  stiffening  girders. 
Since  these  chords  are  cut  at  the  middle,  the  entire  work  of  resisting 
wind  pressure  is  done  by  the  bottom  lateral  system.  The  top  system, 
in  conjunction  with  the  cross-frames  and  hangers  in  a  vertical  plane 
above  each  cross-girder,  serve  simply  to  transfer  the  wind  stresses  and 
a  portion  of  the  load  to  the  bottom  system.  We  may  assume  for  the 
weight  of  the  top  system  500  pounds  per  linear  foot,  and  for  the  cross- 
frames  and  hangers,  1,920  pounds  per  linear  foot,  as  computed  by  the 
New  York  Board.  These  weights  may  be  considered  constant  for  all 
values  of  the  span  within  the  limits  of  this  investigation. 

In  the  bottom  system  the  chords  are  the  bottom  chords  of  the  stiffen- 
ing girders,  in  the  dimensioning  of  which  the  wind  stresses  have 
already  been  provided  for.  The  cross  girders  of  the  floor  system  form 
the  lateral  struts,  and  the  diagonals  are  strained  in  tension.  It  only 
remains  to  determine  the  weighi  per  linear  foot  of  the  diagonals.  The 
depth  of  the  wind-girders  (d)  is  100  feet,  and  the  theoretical  panel 
length  (b)  is  120  feet.    The  number  of  panels  (n)  on  each  side  of  the 

middle  point  is  therefore  ^     The  theoretical  panel  load  is  2,250  b;  the 

assumed  unit  stress  is  25,000  pounds ;  and  25  per  cent  is  added  for  con- 
structive details.  The  weight  of  the  diagonals  per  linear  foot  of  span 
will  then  be 

2x1.25x3.4x2250  b      {b2+d>)  T 

 mwi^iv  =  °*3889  L- 

For  the  weights  in  pounds  per  linear  foot  of  the  lateral  or  sway 
bracing,  including  the  cross-frames  and  hangers,  we  therefore  have 
jp3=2420+0.3889  L. 

WORKING  STRESSES. 


In  determining  the  weights  of  the  two  most  important  members  of 
the  bridge — the  cables  and  the  stiffening  girders — the  Board  have 
assumed  working  stresses  which  are  greater  than  those  generally 
adopted  in  truss  or  arch  bridges  of  moderate  span,  and  which,  there- 
fore, require  explanation. 

The  most  approved  formulas  for  the  determination  of  working 
stresses  are  based  upon  the  experiments  of  Herr  Wohler,  made  for 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


25 


the  Prussian  Ministry  of  Commerce,  and  published  at  Berlin  in  1870.* 
These  experiments  not  only  confirmed  the  earlier  result  obtained  by 
Sir  W.  Fairbairn  and  others,  that  with  repeated  applications  of  a  load 
a  bar  breaks  under  less  than  its  static  breaking  load,  but  they  also 
showed  that  the  breaking  load  varies  inversely  with  the  difference 
between  the  maximum  and  minimum  stresses.  Furthermore,  it  was 
found  that  a  bar  may  be  broken  by  a  still  smaller  fraction  of  the  static 
breaking  load  if  it  is  alternately  strained  in  opposite  directions,  the 
stress  alternating  between  a  positive  and  a  negative  quantity. 

The  principal  formulas  representing  these  results  are  based  upon  two 
radically  different  interpretations  of  the  observed  facts.  In  one  case 
it  is  assumed  that  the  repeated  alternations  of  stress  produce  an  actual 
weakening  of  the  material  which  has  been  called  "  fatigue."  This  view 
is  represented  by  the  Launhardt-Weyrauch  formulas,  which  are  as  fol- 
lows: 

For  stress  in  one  direction — 

For  alternating  positive  and  negative  stresses — 

u  —  s  ,x 
a  =  u(l  -  -—  0 

in  which  $  =  j^!^'^  =  rlie  ratio  of  the  least  to  the  greatest  stress ; 

a  =  breaking  strength  under  the  assumed  conditions,  which  is  to  be 
divided  by  the  factor  of  safety  (generally  3) ;  t  =  breaking  strength 
under  a  static  load;  u  =  the  limiting  strength  (LJrsprungsfestigkeit), 
measured  by  the  greatest  load  the  bar  will  bear  with  an  indefinite  num- 
ber of  alternations  between  0  and  u  without  reversal ;  and  s  =  vibration- 
resistance,  which  is  the  limiting  strength  for  alternations  of  equal  mag- 
nitude with  reversal. 

In  the  othej'  ease  it  is  assumed  that  the  alternations  produce  no 
change  whatever  in  the  molecular  condition  of  the  material,  but  that 
the  increased  effects  are  produced  entirely  by  an  increase  in  the  stresses 
due  to  dynamic  action,  the  stress  being  equal  to  the  load  only  when  all 
the  forces  acting  are  in  static  equilibrium.  This  view  is  represented 
by  the  so-called  dynamic  formula,  which  is 

«=max.  S+7;  (max.  S— min.  S) 

In  this  formula  ?]  is  a  coefficient  depending  upon  the  violence  and 
time-rate  of  the  load-changes. 

The  Launhardt-Weyrauch  formulas  are  based  entirely  upon  Wohler's 
experiments,  and  do  not  take  into  consideration  variations  in  the  rate  or 
violence  of  the  dynamic  action.  Prof.  Fidler  says  that  in  these  experi- 
ments the  load  was  applied  about  four  times  per  minute. 

Prof.  Fidler  has  shown  that  when  the  alternations  are  rapid  (for 
which  case  //=  1)  the  dynamic  formula  represents  Wohler's  experi- 
ments as  accurately  as  the  Launhardt-Weyrauch  formulas.  No  satis 
factory  determination,  however,  has  been  made  of  the  value  of  //  for 
the  various  cases  occurring  in  practice.  In  the  case  of  cross-girders 
and  vertical  suspenders,  which  receive  the  full  action  of  the  elastic 
vibrations  due  to  a  sudden  imposition  of  the  load,  Prof.  Fidler  assumes 
i  =  1,  and  he  adopts  the  same  value  for  the  diagonals  of  the  web  brac- 
ing. For  the  flanges  of  a  girder  or  in  the  principal  members  of  an 
arch  or  suspension  bridge,  in  which  the  stress-changes  take  place  more 
gradually,  he  recommends  a  reduced  value  bearing  some  unknown 


*  Uber  die  Festigkeitsversuche  mit  Eiseii  imd  Stahl. 


26 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


relation  to  the  length  of  span.  He  considers  the  value  r?=  J  to  be  large 
enough  for  all  spans  down  to  about  100  feet. 

It  is  not  possible  in  this  report  to  make  an  extended  comparison  of  the 
merits  of  these  formulas.  It  maybe  remarked, however,  that  the  effects 
of  variations  in  dynamic  action  certainly  play  an  important  part  in  the 
determination  of  ultimate  strength,  although  there  are  as  yet  no  experi- 
ments showing  how  far  this  strength  is  affected  by  the  frequency  as 
distinguished  from  the  mere  number  of  the  stress-changes,  nor  whether 
a  period  of  rest  after  "fatigue"  restores  strength.  These  effects  of 
dynamic  variations,  which  are  entirely  unrepresented  in  the  Launhardt- 
Weyrauch  formulas,  really  exist,  and  are  of  special  importance  in  the 
theory  of  suspension  bridges.  A  clear  and  able  discussion  of  the  whole 
subject  will  be  found  in  Chapter  xiii,  of  Prof.  Fidler's  Practical  Treatise 
on  Bridge  Construction. 

The  Board  have  adopted  for  the  cables  a  working  stress  of  60,000 
pounds,  which  is  one-third  of  the  static  breaking  load.  Prof.  Melan 
says  that,  owing  to  the  lack  of  experiments  with  steel  wires,  we  can 
consider  the  laws  of  Wohler  only  so  far  as  to  allow  for  large  spans  a 
somewhat  greater  value  of  the  working  stress.  For  ordinary  spans  he 
adopts  a  working  strength  of  about  one-fourth  the  ultimate  strength  of 
the  wire.  The  Board  believe  that  a  safety  factor  of  3  is  amply  sufficient 
to  cover  both  the  effects  of  variations  in  stress  and  the  imperfections 
of  manufacture  and  adjustment  in  the  cables.  As  regards  variations 
in  stress,  it  is  to  be  remarked  that  there  are  no  reversals,  the  wire 
being  always  intension;  that  considerable  deflections  correspond  to 
relatively  slight  changes  in  stress -;  and  that  the  stresses  are  slowly  and 
gradually  applied,  and  well  witbin  the  high  elastic  limit. 

This  latter  point  is  of  special  importance,  for  it  is  probable  that 
Wohler's  law  of  reversals  does  not  hold  good  for  stresses  well  within 
the  elastic  limit.  For  example,  in  the  balance  spring  of  a  watch,  ten- 
sion and  compression  succeed  each  other  some  150,000,000  times  in  a 
year,  and  the  spring  works  lor  years  without  apparent  injury.*  In 
this  connection  it  may  be  remarked  that,  although  cables  which  have 
been  long  in  use  have  been  frequently  examined,  no  deterioration  of 
strength  which  could  be  attributed  to  variations  of  stress  has  ever 
been  discovered.  If  we  use  the  Launhardt  formula,  we  are  justified 
in  making  u  very  nearly  equal  to  /. 

If  we  employ  the  dynamic  formula,  the  factor  max.  S — Min.  S  will  be 
very  small,  for  the  reasons  just  given.  As  for  the  coefficient  t?,  we  only 
know  that  it  diminishes  as  the  span  increases,  and,  according  to  Prof. 
Fidler,  it  need  not  be  greater  than  £  for  a  span  as  small  as  100  feet;  it 
must  therefore  be  a  very  small  fraction  for  spans  as  large  as  those  now 
under  consideration.  The  variation- term  of  this  formula  will  probably 
be  so  small  that  it  may  be  safely  neglected. 

As  regards  imperfections  of  manufacture  and  adjustment,  which  are 
covered  in  general  practice  by  the  safety  factor  3,  the  following  points 
are  to  be  noted.  The  uniformity  of  strength  is  greater  for  wire  than 
for  any  other  form  of  steel.  The  process  of  manufacturing  a  wire  cable 
is  in  itself  a  test  of  the  material  and  insures  a  more  nearly  uniform 
distribution  of  stress  over  the  cross-section  than  can  be  obtained  in  any 
other  structure  formed  of  a  very  great  number  of  parts.  If  a  factor 
of  3  is  sufficient  to  cover  the  defects  of  material  and  construction  of  a 
riveted  bridge-member,  a  somewhat  less  factor  ought  to  be  sufficient  for 
a  wire  cable. 


"  Prof.  Ewing,  Strength  of  Materials,  Eiic.  Brit. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


27 


For  the  reasons  above  given,  the  Board  are  of  the  opinion  that  a 
safety  factor  of  3  is  sufficient,  and  have  therefore  adopted  60,000  pounds 
per  square  inch  as  the  working-  stress  for  the  cables. 

The  New  York  Board  adopted  the  same  working  stress,  giving  as 
their  reason  that  this  is  "the  same  proportion  of  the  ultimate  strength 
that  the  20,000  pounds  adopted  in  the  cantilever  structure  bears  to  the 
probable  strength  of  eye-bar  steel.*' 

The  Board  have  adopted  15,000  pounds  per  square  inch  for  the  work- 
ing strength-  of  the  stiffening  girders.  The  Few  York  Board  limited 
the  stresses  due  to  a  moving  load  to  12,500  pounds,  because  there  is  a 
reversal  of  strains,  but  allowed  the  stresses  from  the  combined  effects 
of  moving  load  and  wind  to  run  up  to  22,500  pounds.  The  reasons  of 
this  Board  for  adopting  a  higher  working  stress  in  the  stiffening  gird- 
ers are  as  follows : 

Although  there  is  a  theoretical  reversal  of  strains,  it  will  rarely  and 
perhaps  never  occur  with  the  maximum  stress,  since  this  would  require 
six  of  the  heaviest  freight  trains,  abreast  of  each  other,  to  cross  and 
recross  the  bridge,  first  in  one  direction  and  then  in  the  other.  This 
would  probably  never  happen  on  a  bridge  devoted  principal!}7  to  pas- 
senger traffic,  and  it  could  be  prevented  by  the  simplest  police* regula- 
tions. Again,  the  lower  chords  of  the  girders  have  been  made  of  suf- 
ficient strength  to  resist  the  combined  maximum  stresses  of  the  live 
load  and  the  wind;  but  the  maximum  chord-stresses  could  never  occur 
at  the  same  time,  since  with  the  maximum  wind  pressure  no  trains 
could  cross  the  bridge.  'Some  allowance  has  been  made  for  this  by  the 
adoption  of  a  working'  strength  of  30,000  pounds  for  that  part- of*  the 
material  added  to  resist  wind.  The  only  duty  of  these  girders  is  to 
distribute  the  live  load  and  thus  prevent  inconvenient  deflections.  It 
is  not  necessary  to  give  them  the  margin  of  strength  which  they  would 
require-  if  they  were  essential  to  the  stability  of  the  bridge. 

The  Board  are  of  the  opinion  that  the  great  distinction  between  the 
stable  equilibrium  of  a  suspension  bridge,  which  can  not  break  down 
from  the  failure  of  any  stiffening  member,  and  the  unstable  equilib- 
rium of  a  truss,  arch,  or  cantilever  bridge,  in  winch,  they >fa dure  of  a 
member  may  involve  the  collapse  of  the  entire  bridge,  ought  to  receive 
full  recognition  in  the  adoption  of  unit  stresses  and  safety  factors. 
The  weight  of  the  stiffening  girders  constitutes  the  most  important 
single  element  in  the  suspended  weight?  of  the  bridge,  being  for  the 
maximum  span  about  one-half  the  entire  permanent  load.  It  should 
be  made  no  greater  than  is  absolutely  necessary,  for  the  structure 
ought  not  to  be  kept  under  a  continuous  stress  to  provide  a  larger 
margin  for  stresses  which  may  never  occur.  The  Board  believes  that 
the  working  stresses  adopted  are  amply  sufficient  for  the  members  of 
the  bridge. 

TOWERS. 

The  weight  of  the  towers  forms  no  .part  of  the  suspended  load,  and 
therefore  is  only  indirectly  connected  with  the  question  of*  the  maxi- 
mum span.  There  is,  of  course,  a  practical  limit  to  the  height  to  which 
the  towers  can  be  carried,  and  the  relation  between  their  cost  per  ver- 
tical linear  foot  and  the  cost  of  the  suspension  system  per  linear»foot 
of  span  will  be  an  important  element  in  determining  the  most  econom- 
ical versine  for  the  cables. 

The  towers  will  be  supposed  to  be  formed  of  steel  columns  braced 
together,  and  will  start  from  the  upper  surface  of  the  masonry,  105  feet 
below  the  lowest  point  of  the  cables.    An  empirical  formula,  giving 


28 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  approximate  weight  of  metal  (Wt)  in  the  tpwers,  has  been  deduced 
by  Mr.  Linden  thai  from  various  estimates  of  designs  for  suspension 
bridges,  as  follows: 

Since  the  section  of  the  cable  is  throughout  the  same,  the  tangent  to 
the  cable  at  the  tower  in  the  end  span  should  intersect  a  horizontal 
line  tangent  to  the  cable  curve  at  a  distance  from  the  axis  of  the  tower 
not  greater  than  that  of  the  intersection  of  the  similar  tangent  in  the 
middle  span;  hence  the  end  spans  should  each  beat  least  one-fourth  of 
the  main  span,  and  the  entire  length  of  the  bridge  from  face  to  face  of 
anchorage  should  be  at  least  1.5  L.  Subject  to  this  condition,  the  end 
spans  should  be  made  as  short  as  convenien  t  to  save  cable  weight.  This 
is  also  important,  when  the  backstays  carry  any  directly  suspended 
load,  because  the  bending  moments  from  the  live  load  in  their  stitfening 
girders  may  otherwise  become  greater  than  in  the  main  span.  In  the 
present  investigation,  however,  the  loads  in  the  side  spans  are  supposed 
to  be  supported  from  beneath,  and  the  backstays  have  simply  to  trans- 
mit the  suspended  load  of  the  main  span  to  the  anchorages,  the  pres- 
sure on  the  top  of  each  tower  being  equal  to  the  total  dead  and  live 
load  of  the  main  span. 

Let  La  =  length  of  th^  bridge  exposed  to  wind  pressure  reacting  lat- 
erally on  the  towers,  in  this  case  equal  to  L. 

ht  =  height  of  the  metallic  portion  of  the  towers  from  bedplate  to 
cable  bearing. 

Wa  =  suspended  dead  load  plus  maximum  live  load  per  unit  of  span. 
Et  =  reaction  at  top  of  towers,  =  2  L  WB  (for  both  towers). 
W\  =  weight  of  steel  per  linear  foot  of  square  inch  cross  section  =  3.4 
pounds. 

8=  factor  of  safety.  This  will  be  assumed  as  3. 

u  =  ultimate  strength  of  steel  per  square  inch,  corresponding  vO  S  =  1. 

a  —  coefficient  of  practice,  including  stairways,  housings,  cable  bear- 
ings, etc.,  deduced  from  actual  designs  =  1.65  (Lindenthal). 

Steel  having  an  ultimate  strength  of  from  90,000  to  100,000  pounds 
per  square  inch,  and  an  elastic  limit  from  56,000  to  60,000  pounds,  is 
considered  by  Mr.  Lindenthal  more  suitable  and  economical  for  heavy 
towers  than  a  forgeable  or  punchable  steel,  with  an  ultimate  strength 
of  60,000  pounds.  All  rivet  holes  in  such  high  steel  must  be  drilled  and 
not  punched  and  reamed. 

The  metal  m  the  towers  is  proportional  to  the  reaction  Et  and  the 
height  ht.    The  weight  of  metal  in  the  towers,  exclusive  of  bracing,  will 

therefore  be  — *  —-7  -  -  -• 

The  towers  require  bracing  against  wind  pressure  and  bending  from 
temperature  changes  in  the  cables.  The  metal  in  the  braces  will  be 
proportional  to  the  square  of  the  height  of  the  towers  and  to  the  length 
L  exposed  to  wind  pressure  and  temperature  changes;  hence  the  weight 
of  the  bracing  in  tons  will  be  L  ht2  S  b1  in  which  b  is  the  coefficient  of 
proportional  weight  deduced  from  actual  designs  =  0.001  (Lindenthal). 

The  weight  of  the  towers  will  therefore  be 

Wt=Rt  ht  s  a  Wi+L  ht2  s  b—lit  S  (Rt  a  wx  +  L  ht  b) 
n  u 

Making  *=3,  m1=3.4,  a=  1.65,  &=0.001,  Rt=2  W8L,  and  ^=60000,  we 
obtain  for  the  weight  of  the  towers  in  pounds 

Wt=L7ft  (0.187  W„+7*t) 
333 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


29 


This  is  on  the  assumption  that  the  towers  are  constructed  on  the  plan 
followed  by  the  Xew  York  Board,  so  that  the  cables  may  be  arranged 
side  by  side,  and  that  steel  of  an  ultimate  strength  of  60,000  pounds 
per  square  inch  is  employed  in  their  construction. 


BACKSTAYS. 


The  length  and  consequently  the  weight  of  the  backstays  will 
depend  entirely  upon  the  arrangement  of  the  end  spans,  and  this  will 
in  every  case  be  determined  by  the  local  conditions.  If  I  represents 
the  length  of  a  single  backstay,  the  total  weight  (  Wb)  of  the  backstays 
for  the  whole  bridge  will  be  Wb=2  /  w!  in  which  w'=tihe  weight  of  all 
the  cables  per  linear  foot. 

If  the  backstays  intersect  the  horizontal  plane,  tangent  to  the  cable- 
curve  at  a  distance  i  Lfrom  the  axis  of  the  towers  (which  is  the  most 
economical  arrangement  so  far  as  the  total  amount  of  cable  metal  is 
concerned),  the  length  of  each  stay  from  the  floor  level  to  the  top  of 
the  tower  (the  floor  being  considered  horizontal  and  60  feet  below  the 

lowest  points  of  the  cables)  will  be  5  (^4-  60),  to  which  should  be  added 

o 

a  constant  length  of  about  100  feet  to  carry  the  end  of  the  stay  to  its 
point  of  connection  with  the  anchor  chain,  which  should  be  well  below 
the  floor  level.    For  this  case  the  formula  becomes 

Wb=  (468.3  +  0.559  L)  w'=  (449.6  +  0.537  L)  w. 


ANCHOR  CHAINS  AND  PLATES. 


The  anchor  chains  are  formed  of  steel  eye  bars  and  connect  with 
the  cables  outside  of  the  masonry  of  the  anchorages,  and  with  bearing 
plates  of  rolled  steel  at  their  lower  ends.  They  are  proportioned  for  a 
stress  of  20,000#pounds  per  square  inch  with  an  allowance  of  40  per 
cent  for  the  weight  of  pins  and  constructive  details.  The  tension  on 
each  backstay  is  18,960.000  pounds.  The  weight  of  the  anchor-chains 
per  linear  foot  tor  each  backstay  will  therefore  be 


18,960,000x3.4x1.4     ,  -10  , 
oTTTuwa  =4,ol2  pounds. 


20,000 

The  length  of  each  chain  may  be  assumed  as  200  feet.  The  weight 
of  chains  for  each  backstay  will  therefore  be  902,400  pounds.  The 
weight  of  steel  in  each  anchorage  plate  may  be  assumed  as  100,000 
pounds,  making  the  total  weight  of  anchorage  metal  for  each  back- 
stay 1,002,400  pounds.  If  n  represents  the  number  of  standard  cables 
in  the  bridge,  the  total  weight  of  the  anchorage  metal  (Wa)  will  be 
\Ya  =  2,004,800  n. 

In  this  formula  no  deduction  of  weight  is  made  for  the  diminution  of 
the  tension  due  to  the  friction  of  the  chains  on  their  supports. 

For  the  bridge  of  maximum  span  with  16  standard  cables  we  have 
Wa=32,076,800  pounds=  16,038.4  tons. 


HASONRY  AND  FOUNDATIONS. 


Anchorages. — As  the  anchorage  masonry  acts  merely  as  a  weight,  an 
inexpensive  class  of  masonry  can  be  used  everywhere  except,  perhaps, 
in  the  immediate  vicinity  of  the  bearings  of  anchorage  cables  and 
plates.   The  foundations  need  go  no  deeper  than  necessary  to  obtain  a 


30 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


soil  giving  sufficient  resistance  to  horizontal  sliding,  and  therefore  will 
be  of  comparatively  simple  and  easy  construction. 

Tower  foundations. — The  lower  portion  of  the  towers  above  ground 
and  all  that  below  ground  will  naturally  be  built  of  masonry,  and 
may  be  all  treated  as  constituting  the  tower  foundations.  Being  pro- 
portioned directly  to  the  weight  which  they  have  to  carry,  such  foun- 
dations for  suspension  bridges  differ  from  those  of  other  bridges  only 
so  far  as  affected  by  the  great  height  of  the  towers  proper  and  their 
consequent  great  weight  and  leverage;  and  therefore  are  like  other 
foundations  except  that  they  must  be  given  more  cross-section,  more 
care,  and  a  better  footing  upon  their  beds. 

In  proportioning  such  piers,  the  New  York  Board  adopted  the  fol- 
lowing limits  of  stress: 

The  pressure  between  the  metallic  bed- plates  and  the  top  of  the 
masonry  should  not  exceed  20  tons  to  the  square  foot.  The  pressure 
within  the  masonry  and  on  the  foundation  should  not  exceed  10  tons 
to  the  square  foot;  but  in  determining  these  pressures,  the  weight  of 
materials  displaced  by  the  pier  is  to  be  deducted. 

The  New  York  Board  remark  that  u  while  these  pressures  have  been 
exceeded  in  some  structures,  they  are  higher  than  in  usual  practice, 
and  call  for  masonry  of  good  quality  and  of  more  than  ordinary  cost." 

The  method  of  foundation  construction  will  depend  greatly  upon 
local  considerations.  For  a  bridge  of  maximum  span  these  founda- 
tions should  rest  upon  solid  rock,  if  possible,  and  at  least  upon  hard, 
incompressible  impermeable  soil.  Modern  methods  have  already  estab- 
lished foundations  at  a  level  of  162  feet  below  the  water  surface,  and 
provide  means  for  going  still  deeper,  if  necessary,  and  for  obtaining  a 
properly  leveled  surface  in  the  rock  when  found;  so  that  the  question 
of  foundations  affects  to-day  only  the  economy  and  not  the  engineer- 
ing practicability  of  bridge  construction. 


It  is  now  proposed  to  investigate  the  maximum  length  of  span  prac- 
ticable for  a  suspension  bridge  entirely  from  an  engineering  point  of 
view,  leaving  the  question  of  the  relation  between  traffic  capacity  and 
cost  of  construction  for  subsequent  consideration. 

If  we  suppose  the  cable-curve  to  be  referred  to  rectangular  axes 
through  the  lowest  point  as  an  origin,  we  have  from  the  construction 
of  the  funicular  polygon — 


in  which  Q  represents  the  constant  horizontal  tension  at  any  point  of 
the  polygon,  and  P  the  total  suspended  load  per  linear  foot  of  span. 
The  units  are  the  pound  and  the  foot. 

The  load  P  is  composed  of  the  weights  per  unit  of  span  of  the  live 
load,  track-platform,  bracing,  cables  and  suspenders,  some  of  which 
vary  slightly  with  x\  but  the  Board  has  found  by  a  careful  analysis  that 
even  with  the  unusual  weights  and  spans  considered  in  this  investiga- 
tion, the  error  involved  in  the  assumption  that  P  is  constant  is  too 
small  to  be  of  any  practical  consequence.  It  is  therefore  assumed  that 
the  load  is  uniformly  distributed,  in  which  case  we  obtain  by  integra- 
tion for  the  equation  of  the  cable-curve  y  which  represents  a  par- 


THE  ENGINEERING  PROBLEM  OF  MAXIMUM  SPAN. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


31 


abola.    If  L  represents  the  span  and  R  the  ratio  of  the  span  to  the 

P  L  K 

versine  of  the  cable  we  obtain  Q  =  — 6 — • 

o 

The  greatest  stress  on  the  cables  is  at  their  highest  points,  and  for 
this  maximum  tension  the  strength  of  the  cables  must  be  proportioned. 
Its  horizontal  component  is  the  constant  horizontal  tension  Q  and  its 

vertical  component  is  the  weight  on  the  half  span,  -jr-m  If  T  repre- 
sents this  maximum  stress  we  obtain 


v    -I  8  8 

If  we  represent  by  Li  the  limiting  span,  that  is,  the  span  at  which 
the  cable  will  carry  its  own  weight  with  a  given  stress  per  unit  of  cross- 
section  without  carrying  any  other  load  whatever,  we  obtain  from  the 
above  equation,  by  making  p'=0  and  L=Lj 

t_wJa 
8 

hence 

p'+w_ln 
w   ~~  L 


From  the  above  equations  we  obtain 


1    WR2  +  16. 

For  metallic  towers  and  large  spans  the  value  R=8  will  be  generally 
about  the  most  economical  value  for  the  ratio  of  the  span  to  the  cable 
versine,  when  the  cost  of  the  foundations  is  taken  into  consideration. 
If  we  make  E  =  8  and  substitute  for  T  the  working  strength  per  square 
inch  of  the  material  of  the  cable,  which  we  have  assumed  as  60,000 
pounds,  and  for  w  the  weight  of  a  linear  foot  of  the  cable  measured 
horizontally  and  having  a  cross-section  of  one  square  inch,  which  is 
3.54  pounds,  we  obtain  L: =15100  feet; 
and 

p'  +  w_  15160 
w  L 

The  values  of  p'  and  w  in  pounds,  as  determined  previously,  are  as 
follows : 

p' =13605  +  27761726  Lr1-}-  3.21906  L  +  0.00055335  L2+  0.000000003 L3 
10=17917. 

Substituting  these  values  and  reducing  we  obtain 
31522  L  +  3.21906  L2  +  0.00055335  L3  -j-  0.000000003  L4  =  213S56991, 
the  solution  of  which  gives  for  the  practical  maximum  span 

L=1335  feet. 

This  span  is  measured  between  the  highest  points  of  the  cables  at 
opposite  ends  of  the  bridge. 

The  Board  consider  this  a  conservative  value  of  the  maximum  span, 
as  it  is  based  upon  assumptions  well  within  the  limits  of  theory  and 
experience.  * 
S.  Ex.  1  S 


32 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  elements  of  the  bridge,  deduced  by  the  preceding  formulas,  are 
as  follows: 


Span  between  tops  of  cables  feet..  4,335 

Height  of  towers  above  masonry  :  do. 707 

Number  of  cables   16 

Diameter  of  each  cable  with  wrapping  inches..  21A 

Suspended  iceiglit  per  linear  foot  of  span. 

Pounds. 

Live  load   6,353 

Platform   7,200 

Stiffening  girders   25.202 

Wind  bracing   4.  106 

Cables   17,917 

Cable  wrapping   433 

Suspenders   1,  445 


Total  suspended  weight  per  linear  foot  ,   62,  656 

=  31.  328  tons. 

Tons. 

Suspended  weight  for  whole  middle  span  =   135,  807 

Weight  of  backstays   24,  882 

Weight  of  aut  hor  chains  and  |)lates   16,  038 

Weight  of  towers  .   57, 172 


Total  weight  of  metal  in  the  bridge   233,899 


THE  RELATIONS  BETWEEN  SPAN,  TRAFFIC  AND  COST. 

In  the  preceding  pages  the  Board  have  determined  to  the  best  of 
their  ability  the  maximum  span  practicable  for  a  suspension  bridge 
from  a  purely  engineering  point  of  view.  Their  instructions  further 
require  them  to  investigate  the  maximum  span  "  consistent  with  an 
amount  of  traffic  probably  sufficient  to  warrant  the  expense  of  con- 
struction." This  involves  the  consideration  of  two  subjects;  the  cost 
of  construction  and  the  traffic  capacity  of  the  bridge. 

The  cost  of  a  suspension  bridge  can  not  be  determined  simply  as  a 
function  of  the  span  and  traffic.  In  the  construction  of  every  such 
bridge  there  are  elements  of  cost  which  depend  almost  entirely  upon 
local  conditions,  and  can  not  be  estimated  even  with  the  roughest 
approximation  until  these  conditions  are  fully  known.  For  example, 
the  cost  of  the  piers  will  depend  upon  the  depth  of  the  solid  foundation 
below  the  bottom  of  the  stream  or  the  surface  of  the  ground;  the  cost 
of  the  towers  and  anchorages  will  depend  upon  the  height  at  whicli  it 
is  necessary  to  elevate  the  roadway  above  the-  water  surface,  which 
again  will  depend  upon  the  character  of  the  river  navigation;  the  cost 
of  spaces  for  anchorages,  approaches  and  terminal  facilities  will  depend 
upon  the  local  land  values. 

By  examining  the  detailed  costs  of  several  very  large  bridges,  it  is 
found  that  these indetermiu ate  local  elements  constitute  on  the  average 
more  than  GO  per  cent  of  the  cost  of  such  bridges  in  cities.  It  has  been 
stated  that  in  the  case  of  the  New  York  and  Brooklyn  Bridge,  the  cost 
of  the  bridge  structure  proper  was  only  one-third  of  the  expenditure 
for  the  entire  work.  In  the  case  of  the  suspension  bridge  to  cross  the 
Hudson  at  New  YoTk,  estimated  for  by  the  New  York  Board,  the  local 
elements  determine  about  54  per  cent  of  the  whole  estimated  cost, 
although  the  cost  of  approaches,  terminal  facilities  and  land  are  not 
included. 

The  determination  of  any  relation  between  traffic  capacity  and  the 
cost  of  construction  warranted  thereby  is  equally  difficult.  It  may,  of 
course,  be  assumed  that  the  bridge  of  maximum  span  will  be  constructed 
only  in  a  locality  where  the  conditions  of  commerce  justify  the  belief 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


33 


that  the  traffic  capacity  of  the  bridge  will  be  fully  utilized.  But  in  the 
general  case  it  is  impossible  to  determine  what  charges  the  traffic  will 
bear.  Moreover,  the  construction  of  such  a  bridge  might  be  desirable 
even  if  the  traffic  were  not  likely  to  give  a  sufficient  return  for  the  vast 
sum  invested.  By  the  combined  action  of  railroad  companies,  such  a 
bridge  might  be  built  for  the  general  benefits  resulting  from  increase 
and  facility  of  traffic,  even  though  it  might  fail  to  earn  directly  a  reason- 
able interest  on  its  cost  ;  and  the  enterprise  might  be  assisted  by  adja- 
cent cities,  as  was  done  in  the  case  of  the  New  York  and  Brooklyn 
Bridge. 

But  while  the  Board  have  been  unable  to  arrive  at  definite  conclusions 
in  the  general  case,  they  believe  that  much  may  be  learned  from  the 
study  of  the  problem  as  limited  by  the  conditions  of  a  special  locality, 
and  the  material  for  such  an  inquiry  is  furnished  by  recent  investiga- 
tions in  connection  with  proposed  bridges  across  the  Hudson  River  at 
New  York. 

It  is  said  that  the  number  of  ferry  passengers  crossing  from  New 
Jersey  to  New  York  City  now  exceeds  85,000,000  per  year,  and  the 
passenger  and  freight  traffics  are  growing  rapidly.  It  can  scarcely  be 
doubted  that  a  bridge  in  this  locality  wonld  be  used  to  its  full  capacity. 
Such  a  bridge  wonld,  however,  be  employed  principally  for  passenger 
traffic,  the  facilities  for  moving  freight  on  floats  at  water  level  to  any 
point  on  the  water  fronts  being  ample  and  convenient. 

The  Hudson  River  at  New  York  forms  the  most  important  part  of 
the  interior  harbor.  Its  mid-channel  depth  of  at  least  49  feet,  and  its 
clear  width  of  at  least  2.800  feet  between  pier-head  lines,  make  it  one 
of  the  finest  roadsteads  in  the  world.  It  is  navigated  by  an  enormous 
commerce.  Strong  protests  against  its  obstruction  by  a  pier  in  the 
channel  have  been  made  by  the  commercial  interests  of  the  port.  The 
least  objectionable  location  for  such  an  obstruction  would  be  not  far 
from  the  middle  point,  between  the  pier-head  lines,  where  it  would 
divide  the  upstream  and  downstream  traffic,  but  this  location  is  pro- 
hibited by  the  great  depth  to  a  firm  foundation. 

The  New  York  Board  reported  that  it  is  safe  and  practicable  to  cross 
the  river  with  a  single  span,  and  estimated  the  cost  of  a  suspension 
bridge  for  that  purpose,  its  New  York  pier  being  between  Fifty-ninth  and 
Sixtieth  streets,  at  $30,743,000.  This  is  the  estimate  for  their  Lighter 
Structure,  but  it  provides  for  a  bridge  amply  sufficient  for  the  purposes  for 
which  it  is  intended.  Moreover,  the  estimate  was  made  for  the  purposes 
of  comparison,  and  the  report  of  the  Board  distinctly  states  that  it  is  not 
to  be  taken  as  an  absolute  estimate  of  cost.  This  Board  considers  this 
estimate  perfectly  satisfactory  for  the  purpose  for  which  it  was  made, 
but  they  think  it  desirable  to  determine  a  minimum  as  well  as  a  maxi- 
mum estimate,  to  show  the  variations  to  which  such  estimates  are  liable 
and  how  much  they  are  affected  by  legitimate  differences  in  the  assump- 
tions upon  which  they  are  based.  An  estimate  has  therefore  been  made 
on  the  following  assumptions : 

The  cost  of  structural  steel  is  taken  at  4  cents  per  pound,  in  accord- 
ance with  the  views  of  a  majority  of  the  New  York  Board,  as  indicated 
in  their  report. 

The  cost  of  wire  work  is  taken  at  7  cents  per  pound,  which  is  based 
npon  prices  given  by  leading  manufacturers  and  upon  actual  experi- 
ence in  the  case  of  the  New  York  and  Brooklyn  Bridge. 

The  weights  of  metal  are  determined  by  the  formulas  given  in  this 
report. 

The  bridge  is  supposed  to  be  located  near  Sixty-ninth  street,  New 
S.  Ex.  12  3 


34 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


York,  and  the  cost  of  the  substructure  is  assumed  to  be  the  cost  at  the 
lower  location  (between  Fifty-ninth  and  Sixtieth  street),  as  estimated 
by  the  Xew  York  Board,  less  $2,900,000,  which  they  state  would  be 
saved  by  adopting  the  upper  location.  The  minimum  estimate  is  as 
follows : 

Structural  steel : 

Suspended  weights.  pounds. .  90,  870,  000 

Towers  do....  52,313,000 

Chains  and  anchor  plates  do   18,  324,  000 

Total  do....  161,507,000 

At  4  cents  per  pound   $6, 460,  280 

Wire  work: 

Main  cables  and  wrapping  pounds. .  30,  358,  000 

Backstays  and  wrapping  do   22,  738.  000 

Suspenders  do   3, 222^  000 

Total  do....  56,318,000 

At  7  cents  per  pound   $3,  942, 260 

Cost  of  superstructure   10,  402,  540 

Cost  of  substructure   11,  784,  000 

Total  cost  of  bridge   22, 186,  540 

The  final  plans  for  a  work  of  such  magnitude  would  only  be  adopted 
after  the  most  extended  theoretical  and  experimental  investigations, 
and  the  estimated  cost  would  undoubtedly  be  much  reduced  by  such 
studies.  Assuming  the  most  favorable  location  and  the  most  compe- 
tent engineering  management,  the  Board  believe  that  $23,000,000  is  a 
reasonable  estimate  for  a  six-track  railroad  suspension  bridge  3,200  feet 
long,  and  they  consider  the  amount  of  traffic  which  such  a  bridge  would 
accommodate  sufficient  to  warrant  the  expense  of  construction.  They 
believe,  however,  that  the  bridge  should  be  so  constructed  that  its 
capacity  can  be  readily  increased,  and  with  the  suspension  system  this 
can  be  provided  for  by  giving  suitable  dimensions  to  the  towers  and 
anchorages. 

If  sufficient  inducements  were  offered  to  competent  engineers  to  pre 
pare  competitive  designs  and  estimates  for  a  single- span  bridge  at  this 
locality,  the  Board  do  not  doubt  that  perfectly  satisfactory  plans  would 
be  obtained  within  the  limit  of  cost  of  the  estimate  given  above. 

The  Board  desire  to  express  their  obligations  to  Mr.  Gustav  Linden- 
thai,  C.  E.,  Mr.  W.  Hildenbrand,  O.  E.  and  Mr.  L.  L.  Buck,  O.  E.  for 
information  and  valuable  suggestions. 

The  following  appendices  accompany  this  report  : 

Appendix  A. — Orders  and  instructions. 

Appendix  B. — Correspondence  with  wire  manufacturers. 

Appendix  C. — Wind  pressure. 

Appendix  D. — Temperature  Strains  in  Three  Hinged  arches,  by  Gustav  Linden- 
thai,  C.E. 

Appendix  E. — The  Theory  of  the  Stiffening-  Girder,  by  Prof.  J.  Melan. 

Respectfully  submitted. 

C.  W.  Raymond, 
Major,  Corps  of  Engineers. 

Wi.  H.  Bixby, 
Captain,  Corps  of  Engineers. 

Edw.  Burr, 
CaptaifZ,  Corps  of  Engineers. 

Brig.  Gen.  Thomas  L.  Casey, 

Chief  of  Engineers,  U.  8.  A. 


REPORT 


OF 


BOARD  OF  EXGIXEEES 


9 


NEW  YORK  AND  NEW  JERSEY  BRIDGE. 


So 


Extract  from  act  of  Congress  entitled  "An  Act  To  authorize  the  New  York  and  New 
Jersey  Bridge  Companies  to  construct  and  maintain  a  bridge  across  the  Hudson  River 
beUveen  New  York  City  and  the  State  of  New  Jersey,"  approved  June  7, 1894. 


Be  it  enacted  by  the  Senate  and  House  of  Representatives  of  the  United  States  of  America 
in  Congress  assembled,  That  *  *  *  the  President  shall  appoint  a  hoard,  consist- 
ing of  five  competent,  disinterested,  expert  bridge  engineers,  of  whom  one  shall  be 
either  the  Chief  of  Engineers  or  any  member  of  the  Corps  of  Engineers  of  the  United 
States  Army,  and  the  others  from  civil  life,  who  shall,  within  thirty  days  after  their 
appointment,  meet  together  and,  after  examination  of  the  question,  shall,  within 
sixty  days  after  their  first  meeting,  recommend  what  length  of  span,  not  less  than 
two  thousand  feet,  would  be  safe  and  practicable  for  a  railroad  bridge  to  be  con- 
structed over  said  river,  and  file  such  recommendation  with  the  Secretary  of  War, 
but  it  shall  not  be  final  or  conclusive  until  it  has  received  his  written  approval.  In 
case  any  vacancy  shall  occur  in  said  board,  the  President  shall  fill  the  same.  The 
compensation  and  expenses  of  said  board  of  engineers  shall  be  fixed  by  tne  Secre- 
tary of  War  and  paid  by  the  said  bridge  companies,  which  said  companies  shall 
deposit  with  the  Secretary  of  War  such  sum  of  money  as  he  may  designate  and 
require  for  such  purpose :  Provided,  always,  That  nothing  herein  contained  shall  be 
construed  as  preventing  the  said  board  of  engineers  from  meeting,  investigating, 
and  filing  their  recommendation  after  the  expiration  of  said  time  herein  mentioned. 


MEMBERS  OF  BOARD  APPOINTED  BY  THE  PRESIDENT. 


C.  W.  Raymond, 

Major,  Corps  of  Enqineers,  TJ,  S.  Army. 
Mr.  G.  Bouscaren. 


Mr.  W.  H.  Burr. 

Mr.  Theodore  Cooper. 

Mr.  Geo.  S.  Morison. 


36 


REPORT 


OF 

BOARD  OF  ENGINEERS  ON  NEW  YORK  AND  NEW 
JERSEY  BRIDGE. 


Office  of  the  Chief  of  Engineers, 

United  States  Army, 
Washington,  D.  C,  September  29,  1894. 
Sir:  Beferring  to  report,  dated  August  23,  1894,  by  the  Board 
appointed  under  the  provisions  of  the  act  of  Congress  of  June  7,  1894, 
to  consider  length  of  span  of  proposed  bridge  across  Hudson  Eiver 
between  Fifty-ninth  and  Sixty -ninth  streets,  Sew  York  City,  I  beg  to 
recommend  that  500  copies  of  the  report  of  the  Board  be  printed  at  the 
Government  Printing  Office. 

Very  respectfully,  your  obedient  servant. 

Thos.  Lincoln  Casey, 
Brig.-Gen.,  Chief  of  Engineers. 

Hon.  D.  S.  La^iont, 

Secretary  of  War, 

Approved: 

Daniel  S.  Lamont, 

Secretary  of  War, 


REPORT  OF  BOARD  OF  ENGINEERS. 

New  York,  August  23,  1894. 
Sir:  The  Board  of  Bridge  Engineers  appointed  by  the  President 
under  the  act  of  Congress,  approved  June  7, 1891,  authorizing  the  New 
York  and  New  Jersey  Bridge  companies  to  construct  a  bridge  across 
the  Hudson  Eiver,  met  at  the  Army  Building,  New  York  City,  on  Mon- 
day. June  25. 

Your  Board  organized  by  electing  Maj.  C.  W.  Baymoud,  Corps  of 
Engineers,  U.  S.  A.,  chairman,  and  Mr.  Cooper,  secretary. 

Your  Board  began  the  examination  of  the  question  submitted  to  them 
and  gave  it  careful  and  continuous  consideration  up  to  the  present 
time ;  they  have  held  29  regular  meetings. 

Your  Board  personally  visited  and  examined  the  site  of  the  proposed 
bridge  as  defined  by  the  act. 

They  applied  to  the  New  York  and  New  Jersey  Bridge  companies 
for  their  surveys,  borings,  plans,  estimates,  and  such  other  data  as 
referred  to  the  proposed  bridge.    The  surveys  and  borings  furnished 

37 


38 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


upon  this  application  having  been  made  for  a  former  location  not  within 
the  limits  stated  in  the  act,  other  surveys  and  borings  upon  lines 
within  these  limits  were  made  at  the  request  of  the  Board. 

The  New  York  and  New  Jersey  Bridge  companies,  by  their  engi- 
neering representative,  Mr.  Charles  Macdonald,  presented  plans  pre- 
pared by  the  Union  Bridge  Company  tor  the  proposed  bridge,  with  a 
statement  as  to  cost,  estimated  traffic,  and  other  data,  which  are  given 
in  Appendix  B. 

During  the  sessions  public  hearings  were  given  to  a  special  com- 
mittee of  the  New  York  Chamber  of  Commerce,  through  its  chairman, 
Mr.  Gustav  H.  Schwab,  and  its  engineering  counsel,  Mr.  W.  Hilden- 
brand,  and  also  to  Mr.  G.  Lindenthal,  chief  engineer  of  the  North 
Biver  Bridge  Company.  Their  statements  will  be  found  in  Appen- 
dixes C  and  D. 

The  duties  of  your  Board  as  prescribed  by  the  act  are  to  "  recom- 
mend what  length  of  span,  not  less  than  2,000  feet,  would  be  safe  and 
practicable  for  a  railroad  bridge,  to  be  constructed  over  said  river." 
The  act  provides  that  this  bridge  "shall  not  be  located  below  Fifty- 
ninth  street,  New  York  City,  nor  above  Sixty-ninth  street,  New  Y^ork 
City."  Your  Board,  therefore,  understand  their  duties  to  be  to  recom- 
mend what  length  of  span,  not  less  than  2,000  feet,  would  be  safe  and 
practicable  for  a  railroad  bridge  to  be  constructed  over  the  Hudson 
River  between  Fifty-ninth  and  Sixty-ninth  streets  in  the  city  of  New 
York. 

In  making  comparative  estimates,  your  Board  selected  a  location 
midway  between  Fifty-ninth  and  Sixtieth  streets,  but  the  difference 
between  this  location  and  one  further  north  within  the  limits  of  the 
act  has  been  considered  so  far  as  it  affects  the  general  conclusions. 

The  minimum  length  of  span  which  may  be  considered  is  2,000  feet, 
which  your  Board  have  interpreted  as  meaning  2,000  feet  in  the  clear. 
The  maximum  length  of  span  would  be  a  clear  span  between  the  pier- 
head lines,  this  distance  varying  from  3,130  feet  at  Fifty-ninth  street 
to  3,080  feet  at  Sixty-ninth  street. 

The  objections  which  have  been  raised  to  a  pier  in  the  river  apply 
with  equal  force  to  any  pier  located  between  the  end  of  a  2,000-foot 
span  and  the  pier-head  line,  the  pier  being  objected  to  as  interfering 
with  the  use  of  the  river  for  harbor  purposes  rather  than  for  through 
navigation.  The  plans  submitted  to  your  Board  have  located  the  2,000- 
foot  span,  in  accordance  with  the  requirements  of  the  New  YAork  char- 
ter, next  to  the  New  York  pier-head  line,  thus  placing  the  west  pier 
about  1,000  feet  from  the  New  Jersey  pier-head  line;  if  the  span  is 
increased  beyond  2,000  feet  any  injury  done  to  the  harbor  by  obstructing 
the  approach  to  piers  on  the  New  Jersey  shore  would  be  greater  than 
any  benefit  gained  by  increased  width  of  channel  span.  Your  Board 
have  considered  that  navigation  would  not  be  benefited  by  making  a 
span  of  greater  length  than  2,000  feet,  unless  such  span  could  reach  from 
pier-head  line  to  pier-head  line;  they  have  therefore  confined  their 
examination  to  a  span  of  2,000  feet  in  the  clear,  as  compared  with  such 
single  span.  It  must  be  noted,  however,  that  the  pier-head  lines  are 
artificial  and  are  subject  to  change  under  existing  laws.  The  width 
between  pier-head  lines  at  this  location  is  about  400  feet  greater  than 
at  a  point  2  miles  below.  A  small  encroachment  beyond  these  pier -head 
lines  could  be  permitted  without  essential  harm;  it  would  obstruct 
navigation  no  more  than  a  vessel  lying  across  the  head  of  a  pier;  a 
span  of  3,100  feet  in  the  clear  would  meet  all  the  requirements  of  a 
single  span. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


39 


The  plans  submitted  by  the  bridge  companies  provide  for  a  cantilever 
bridge  carrying  six  railroad  tracks.  This  number  of  tracks  is  the  least 
that  has  been  proposed  by  any  company  which  has  contemplated  bridg- 
ing the  Hudson  River  opposite  the  city  of  iSew  York.  Your  Board 
have  therefore  thought  it  right  to  make  estimates  for  a  bridge  furnish- 
ing this  accommodation. 

The  fact  that  the  river  must  be  kept  unobstructed  during  erection 
limits  the  plans  to  cantilever  and  suspension  bridges.  The  plans  sub- 
mitted by  the  bridge  companies  provide  for  a  steel  cantilever  bridge,  a 
description  of  which  is  given  in  Appendix  B. 

A  cantilever  bridge  is  a  rigid  structure,  subject  to  those  changes  of 
shape  only  which  are  due  to  strains;  it  is  well  adapted  to  railroad  uses. 

In  the  first  place,  your  Board  are  of  the  unanimous  opinion  that  a 
cantilever  span  of  3,100  feet  in  the  clear  could  be  built  and  would  be  a 
safe  structure. 

In  the  second  place,  your  Board  have  considered  that  the  practica- 
bility of  such  a  structure  would  depend  upon  its  cost,  and  to  determine 
this  practicability,  have  made  comparative  estimates  of  the  cost  of  two 
cantilever  bridges  with  clear  spans  of  2,000  and  3,100  feet,  respectively. 
These  estimates  are  comparative  rather  than  absolute;  the  benefit  of 
the  doubt,  where  any  exists,  has  been  given  to  the  longer  span.  The 
estimates  include  both  substructure  and  superstructure,  but  have  been 
made  in  round  numbers  and  do  not  include  the  cost  of  tracks  and  other 
features  which  would  be  common  to  both  plans. 

A  series  of  borings,  covering  virtually  the  limits  permitted  by  the  act, 
have  been  made  by  the  bridge  companies  under  the  direction  of  Mr.  C. 
B.  Brush,  c.  E.,  at  the  request  of  your  Board,  to  determine  the  character 
of  the  bottom  of  the  river. 

These  borings  have  found  rock  at  varying  depths,  but  as  the  borings 
were  not  extended  into  the  rock,  the  absolute  information  before  your 
Board  is  that  no  rock  exists  above  the  reported  elevation  rather  than 
that  solid  rock  Exists  below  it;  but  your  Board  have  considered  them- 
selves justified  in  assuming  that  it  is  a  substantial  rock,  suitable  for 
foundations.  The  borings  outside  the  limits  of  the  special  line  consid- 
ered have  confirmed  the  accuracy  of  the  others. 

The  depth  to  rock  is  about  125  feet  at  each  pier-head  line;  it  is  about 
260  feet  at  the  site  where  the  pier  of  the  2,000-foot  span  bridge  would 
come;  the  rock  rises  rapidly  from  each  pier-head  line  shoreward.  The 
depth  of  water  at  the  site  of  the  river  pier  is  about  50  feet.  Under 
the  water  is  a  layer  of  mud  or  silt  about  100  feet  deep.  Below  this 
mud  is  a  fine  sand  filled  with  fresh  water  under  a  pressure  exceeding 
the  head  due  to  its  depth. 

The  mud  or  silt  is  not  a  suitable  material  for  the  foundation  of  bridge 
piers.  For  the  comparatively  moderate  weights  carried  by  bridges  of 
usual  dimensions,  the  sand  would  be  a  suitable  foundation.  For  the 
extraordinary  weights  and  dimensions  of  the  bridge  authorized  by  the 
act.  your  Board  arc  not  satisfied  that  the  piers  would  be  safe  unless 
founded  on  rock,  and  the  comparative  estimates  have  been  made  for 
rock  foundations. 

The  lateral  provisions  to  resist  wind  and  the  longitudinal  provisions 
for  stability  during  erection  require  a  considerable  base:  the  plans  sub- 
mitted by  the  bridge  companies  propose  to  use  a  pier  consisting  of  four 
cylinders  placed  200  feet  between  centers  in  each  direction.  The  total 
reaction,  including  the  effects  of  wind  pressure,  carried  on  each  cylin- 
der is  estimated  at  25,000  tons. 


40 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


In  proportioning  these  piers,  your  Board  have  found  it  necessary  to 
adopt  limits  of  stress.  They  have  based  their  estimates  on  the  suppo- 
sition that  the  pressure  between  the  metallic  bedplates  and  the  top  of 
the  masonry  should  not  exceed  20  tons  to  the  square  foot,  and  that 
the  pressure  within  the  masonry  and  on  the  foundation  should 
nowhere  exceed  10  tons  to  the  square  foot;  they  consider,  however,  that 
in  determining  these  pressures  the  weight  of  the  material  displaced 
should  be  deducted.  The  weight  of  masonry  per  cubic  foot  was  taken 
at  150  pounds  in  air,  at  87  pounds  in  water,  at  50  pounds  in  mud,  and 
at  30  pounds  in  sand.  While  these  pressures  have  been  exceeded  in 
some  structures,  they  are  higher  than  usual  practice  and  call  for 
masonry  of  good  quality  and  more  than  ordinary  cost. 

Your  Board  have  assumed  that  the  masonry  would  finish  50  feet 
above  water,  and  have  estimated  the  cost  of  these  piers,  including 
excavation  and  sinking,  at  $1  per  cubic  foot  above  a  plane  125  feet 
below  water,  and  have  added  8  mills  to  this  price  for  each  additional 
foot  of  depth. 

2,000-FOOT  CLEAR-SPAN  CANTILEVER. 

The  east  pier  of  the  bridge,  with  a  clear  span  of  2,000  feet,  would 
be  immediately  back  of  the  New  York  pierhead  line,  where  the  rock  is 
125  feet  below  mean  high  water.  The  west  pier  would  come  in  the  river, 
where  the  rock  is  260  feet  below  mean  high  water.  The  east  anchorage 
would  be  within  the  shore  line,  where  the  rock  is  not  more  than  20  feet 
below  mean  high  water,  and  the  west  anchorage  would  be  immediately 
west  of  the  New  Jersey  pierhead  line,  where  the  rock  is  125  feet  below 
mean  high  water.  The  site  of  the  west  anchorage  calls  for  an  anchor- 
age span  100  feet  longer  than  is  shown  on  the  plans  submitted  by  the 
bridge  companies. 

The  east  pier  would  consist  of  four  cylinders,  each  containing  866,000 
cubic  feet,  and  costing  on  the  basis  0ven  above.  $866,000,  making  for 
the  four  cylinders,  $3,464,000. 

At  the  site  of  the  west  pier  the  average  depth  to  rock  is  not  less 
than  260  feet.  A  foundation  carried  to  rock  here  would  be  nearly  100 
feet  deeper  than  any  foundation  which  has  ever  been  put  in.  Such  a 
foundation  involves  very  careful  consideration,  and  your  Board  believe 
that  the  additional  price  allowed  for  so  much  of  the  work  as  is  more 
than  125  feet  below  water  is  none  too  large.  Each  of  the  four 
cylinders  would  contain  1,880,000  cubic  feet,  of  which  1,014,000  would 
be  more  than  125  feet  below  water,  making  the  cost  of  each  cylinder 
$2,427,500,  and  the  cost  of  the  four  cylinders  $9,710,000. 

The  east  anchorage  pier  would  be  founded  on  rock  about  20  feet 
below  mean  high  water,  and  the  west  pier  on  rock  125  feet  below  water. 
Each  of  these  piers  has  been  estimated  on  the  basis  of  a  pier  finishing 
150  feet  above  high  water,  20  feet  thick,  and  100  feet  long  on  top,  built 
with  a  batter  of  1  in  20,  and  founded  on  a  caisson  40  by  120  feet  for 
the  east  pier  and  45  by  125  feet  for  the  west  pier.  Taking  the  cost  of 
the  work  above  water  at  75  cents  per  cubic  foot,  and  of  the  work  below 
water  at  $1,  the  cost  of  the  east  pier  becomes  $431,000  and  that  of  the 
west  pier  $1,038,000. 

The  cost  of  the  substructure  for  the  bridge,  with  the  2,000-foot  clear 
span,  would  then  be: 


East  anchorage   $-131.  000 

East  pier   3,464,000 

West  pier   9,710,000 

West  anchorage   1,  038,  000 


Total   14, 643,  000 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


41 


A  careful  estimate  prepared  by  the  bridge  companies  makes  the 
weight  of  the  superstructure  230,000,000  pounds,  including  the  main 
span,  the  towers,  and  the  two  anchorage  spans,  covering  a  total  length 
of  4,120  feet.  This  weight  has  been  checked,  and  may  be  taken  as 
approximately  correct.  The  plan  was  prepared  for  a  location  at  Seventy- 
second  street,  where  the  distance  between  pierhead  lines  is  3,070  feet. 
At  Fifty-ninth  street  the  west  anchorage  span  would  be  lengthened 
100  feet,  and  if  the  bridge  is  kept  symmetrical  the  whole  length  will  be 
increased  to  4,320  feet,  and  the  total  weight  to  about  240,000,000  pounds. 
This  estimate  is  based  on  a  moving  load  of  3,000  pounds  per  foot  of 
track  and  on  maximum  working  stresses  of  from  20,000  to  22,500  pounds 
per  square  inch,  or  about  one-third  of  the  ultimate  strength  of  the 
material;  240,000,000,  at  4£  cents  per  pound,  would  cost  $10,800,000. 
The  cost  of  this  bridge  would  then  be  $25,443,000. 

This  is  the  cost  of  a  cantilever  bridge  of  the  minimum  span  which 
your  Board  are  authorized  to  consider,  the  length  of  the  entire  structure, 
from  anchorage  to  anchorage,  being  4,320  feet.  As  this  plan  of  bridge 
is  the  one  which  the  New  York  and  New  Jersey  Bridge  companies 
have  selected  as  the  bridge  they  wish  to  build,  its  cost  must  be  accepted 
for  present  purposes  as  the  cost  of  a  practicable  structure. 

3,100-FOOT  CLEAR-SPAN  CANTILEVER. 

The  site  of  the  east  pier  for  the  span  of  3,100  feet  in  the  clear  would 
be  the  same  as  that  for  the  2,000-foot  span;  the  site  of  the  west  pier 
would' be  the  same  as  that  of  the  west  anchorage  for  the  2,000-foot 
span:  botli  piers  would  be  founded  at  practically  the  same  depth,  or 
125  feet  below  mean  high  water. 

The  weight  of  the  trusses  of  the  long  span  would  be  about  three  times 
the  weight  of  those  of  the  short  span,  and  the  weight  of  the  floor  and 
moving  load  would  be  about  one  and  a  half  times  that  of  the  short  span. 
The  total  reacticfn  on  the  piers  would  be  at  least  two  and  one-half  times 
that  of  the  short  span.  On  this  supposition  each  of  the  four  cylinders 
would  have  to  carry  62,500  tons. 

The  piers  in  both  bridges  are  so  large  that  their  volume  can  be  pro- 
portioned directly  to  the  weights  they  have  to  carry.  This  would  make 
the  volume  of  each  pier  of  the  3,100-foot  span  bridge  two  and  one  half 
times  that  of  the  east  pier  of  the  2,000-foot  span  bridge.  The  estimated 
cost  of  the  east  pier  of  the  2,000-foot  span  bridge  was  83,404,000,  so 
that  we  may  estimate  the  cost  of  each  of  the  two  piers  of  the  3,100- 
foot  span  bridge  at  $8,660,000. 

The  anchorage  piers  required  for  the  long-span  bridge  need  be  little 
larger  above  the  water  level  than  for  the  shorter  span.  The  anchorage 
pier  on  the  east  side  would  be  on  rock  about  20  feet  below  mean  high 
water:  its  cost  would  be  about  the  same  as  that  for  the  2,000-foot  span. 
The  anchorage  pier  on  the  west  side  would  be  on  rock  40  feet  below 
mean  high  water,  and  is  estimated  to  cost  8527.000. 

The  total  cost  of  the  substructure  for  the  3,100-foot  clear  span  bridge 
would  then  be : 


East  anchorage   $431,  000 

East  pier   8,  660.  000 

West  pier   8,  660,  000 

West  anchorage   527.000 


Total   18,278,000 


42 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


Estimates  made  by  this  board  show  that  the  weight  of  the  super- 
structure of  this  bridge  would  be  approximately  730,000,000  pounds, 
about  three  times  that  of  the  shorter  span  bridge ;  730,000,000  pounds 
at  4J  cents  per  pound  is  $32,850,000. 

The  total  cost  of  the  3,100-foot  span  bridge,  covering  a  length  of 
6,100  feet  from  anchorage  to  anchorage,  may,  therefore,  be  estimated  at 
$51,128,000,  though  this  estimate  is  probably  too  low. 

The  estimated  cost  of  the  2,000-foot  span  bridge  was  $25,443,000  for 
4,320  feet;  to  bring  it  into  proper  comparison  with  the  longer  span 
bridge  1,780  feet  of  viaduct  must  be  added;  estimating  this  viaduct  at 
$1,000  a  foot,  the  cost  becomes  $27,223,000.  The  estimated  cost  of  the 
long-span  cantilever  bridge  is  $23,905,000  more  than  this  amount. 

Your  Board  are  of  the  opinion  that  the  additional  cost  of  the  long- 
span  cantilever  bridge  is  so  great  that  it  must  be  considered  imprac- 
ticable. 

SUSPENSION  BRIDGE. 

A  suspension  bridge  is  another  possible  form  of  construction  at  this 
location;  like  the  cantilever,  it  can  be  erected  without  false  work; 
unlike  the  cantilever,  it  has  not  generally  been  considered  well  adapted 
to  railroad  uses. 

It  has  less  rigidity  than  the  cantilever,  and  deflects  more  from  the 
combined  effect  of  temperature  and  load;  the  flexibility  of  the  cables 
tends  to  cause  vertical  undulations  of  the  platform  under  a  moving 
load,  which  are  more  objectionable  for  a  railroad  bridge  than  for  a 
highway  bridge,  where  the  live  load  is  less  concentrated  and  is  applied 
less  rapidly;  these  objections  lessen  in  importance  as  the  span  of  the 
bridge  and  the  proportion  of  the  dead  to  the  live  load  increase. 

In  a  bridge  with  six  independent  tracks  the  condition  of  railroad 
service  approaches  that  of  highway  service,  and  the  position  of  trains 
which  will  produce  a  maximum  disturbance  would  be  of  very  rare  occur- 
rence. The  inclination  of  the  platform  longitudinally  and  transversely, 
arising  from  the  undulations  of  the  cables  under  the  effect  of  moving 
trains,  can  be  reduced  within  unobjectionable  limits  by  a  proper  system 
of  stiffening;  the  effect  of  wind  on  cables  and  platform  can  be  taken 
care  of  by  cradling  the  cables  and  by  a  lateral  system  of  bracing  in  the 
platform  similar  to  that  used  in  truss  bridges.  A  single  railroad  track 
suspension  bridge  of  850-foot  span  has  been  in  continuous  use,  under 
restrictions  of  load  and  speed, for  nearly  forty  years  at  Niagara;  with 
this  example  before  us,  a  six-track  railroad  suspension  bridge  of  3,100 
feet  clear  span  can  not  be  dismissed  without  careful  consideration. 

Your  Board  have  therefore  investigated  such  suspension  bridge  with 
great  care,  and  it  is  their  opinion  that  it  could  be  built  and  that  it  would 
be  a  safe  structure.  As  this  opinion  may  be  thought  a  departure  from 
general  opinion  as  to  the  adaptability  of  the  suspension  bridge  to  rail- 
road service,  it  is  proper  that  the  Board  should  state  their  reasons  there- 
for, and  explain  the  features  of  the  plan  adopted  by  them  for  a  com- 
parative estimate  in  more  detail  than  was  done  for  the  cantilever  plans. 

The  essential  differences  between  a  cantilever  and  a  suspension 
bridge  are,  (1)  that  in  place  of  the  compression  chords  of  the  cantilever 
we  have  land  anchorages  built  of  eyebars  and  masonry;  (2)  in  place 
of  the  tension  chords  of  the  cantilever  we  have  cables  built  of  wire  of 
a  superior  grade  of  metal;  (3)  in  place  of  the  web  bracing  of  the 
cantilever  we  have  a  composite  system  of  suspenders  and  stiffeners. 

No  question  can  be  raised  as  to  the  safe  and  permanent  character  of 
the  anchorages  if  built  with  a  sufficient  factor  of  resistance  and  proper 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


43 


provisions  for  thorough  protection  of  the  anchor  chains  against  rust- 
ing; they  have  the  advantage  over  the  compression  chords  of  the  can- 
tilever that  their  weight  is  supported  directly  on  the  ground,  instead 
of  forming  a  part  of  the  dead  load  to  be  carried. 

As  regards  safety  and  efficiency,  the  wire  cables  are  fully  equal  to 
eyebar  chords,  if  built  with  the  same  margin  of  strength ;  experience 
shows  that  they  can  be  effectively  protected  against  rusting  by  wire 
wrapping  and  painting;  wire  at  least  three  times  as  strong  as  eyebar 
steel  is  a  merchantable  article,  and  cables  made  of  this  wire  have  the 
advantage  over  eyebar  chords  of  less  weight  to  be  carried  by  the 
superstructure. 

The  objections  made  to  suspension  bridges  arise  only  from  the  third 
difference.  It  is  often  claimed  that  a  sufficient  degree  of  rigidity  can 
not  be  secured  for  railroad  purposes,  and  that  the  stiffening  members 
can  not  be  properly  proportioned,  owing  to  the  uncertainty  which  exists 
in  the  intensity  of  stresses  due  to  changes  of  temperature  and  elastic 
deformation  in  the  composite  system.  The  Board  has  given  careful 
consideration  to  these  objections  and  believe  that  for  practical  purposes 
they  are  met  in  the  plan  selected. 

Three  principal  methods  have  been  employed  to  secure  greater 
rigidity  in  suspension  bridges ;  (1)  by  inclined  stays  extending  from 
the  top  of  the  towers  to  the  platform — this  system  was  advocated  and 
applied  extensively  by  the  late  John  A.  Roebling;  (2)  by  trussing  the 
cables  either  with  straight  chords,  as  in  the  Point  bridge  at  Pittsburg, 
or  by  a  system  of  braces  between  two  cables,  as  proposed  by  Mr.  G. 
Linden  thai  for  his  projected  North  River  bridge;  (3)  by  a  stiffening 
girder  fastened  to  the  platform  and  extending  from  one  tower  to  the 
other;  this  system  is  a  feature  common  to  nearly  all  suspension  bridges, 
but  has  seldom  been  applied  in  the  most  approved  form  to  give  the 
best  results.  The  first  method  is  at  best  incomplete,  as  a  stiffening 
truss  must  be  used  for  the  middle  half  of  the  span.  The  second 
method  might  pr«fve  the  most  economical,  but  its  application  to  wire 
cables  is  still  untried.  Your  Board  have,  therefore,  selected  the  third 
method,  that  of  stiffening  the  truss. 

The  suspension  bridge  which  your  Board  have  selected  for  this  loca- 
tion would  consist  of  a  single  span  of  3,200  feet  between  saddles,  thus 
giving  about  3,100  feet  in  the  clear,  the  two  towers  being  located  at 
the  pierhead  lines,  and  the  cables  being  carried  in  straight  lines  from 
the  top  of  the  towers  to  the  anchorages,  making  equal  angles  on  each 
side  of  the  towers.  This  form  of  bridge  has  no  side  spans,  but  the 
tracks  would  be  carried  on  viaducts  between  the  towers  and  the  anchor- 
ages. While  the  use  of  cables  outside  the  towers  to  sustain  side  spans 
is  generally  considered  economical,  the  arrangement  selected  gives  the 
least  length  of  cable  and  reduces  deflection  from  strains  and  tempera- 
ture to  a  minimum. 

The  two  towers  would  be  located  in  practically  the  same  position  as 
the  towers  of  the  3,100-foot  cantilever.  The  substructure  would  be  of 
masonry,  finishing  at  the  same  height  as  the  masonry  of  the  cantilever 
bridge  piers. 

The  towers  themselves  would  be  of  steel  and  would  be  570  feet  high 
from  top  of  masonry  to  saddles,  or  620  feet  from  surface  of  water. 
For  towers  of  this  height  there  is  no  question  of  the  economy  and 
expediency  of  using  metallic  construction. 

The  anchorages  would  be  of  masonry,  each  located  about  1,000  feet 
back  of  the  towers.  Both  towers  and  anchorages  would  have  to  be 
founded  on  rock. 


44 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  cables  would  be  of  wire,  and  the  plans  have  been  based  on 
cables  containing  about  6,000  No.  3  wires  (0.259  inch  in  diameter). 
Wireinakers  are  prepared  to  furnish  a  wire  of  this  size  of  a  guaran- 
teed strength  of  180,000  pounds  per  square  inch  at  moderate  prices 
and  a  much  stronger  wire  at  a  higher  price.  Your  Board  have  adopted 
as  the  unit  stress  on  cables  made  of  straight  wire  of  this  character 
60,000  pounds  per  square  inch,  or  one-third  of  the  breaking  stress, 
this  being  the  same  proportion  of  the  ultimate  strength  that  the  20,000 
pounds  adopted  in  the  cantilever  structure  bears  to  the  probable 
strength  of  eyebar  steel. 

Your  Board  have  estimated  on  a  versed  sine  of  400  feet,  or  one-eighth 
of  the  span.  In  the  East  Eiver  bridge  the  versed  sine  is  less  than 
one-twelfth  of  the  span  and  about  the  same  as  in  other  long-span  sus- 
pension bridges.  In  the  East  Biver  bridge  the  cables  are  of  steel  wire 
and  the  towers  of  masonry.  With  the  introduction  of  steel  toAvers, 
the  economical  proportions  are  changed,  and  it  becomes  practicable  to 
adopt  a  greater  versed  sine  than  has  hitherto  been  considered  wise. 

Stiffening  truss. — There  are  several  admissible  forms  of  stiffening 
truss;  to  justify  the  particular  form  selected  by  the  Board  for  their 
estimate  it  is  proper  to  give  a  short  explanation  of  its  duties  and  mode 
of  action. 

A  stiffening  truss  is  a  girder  supported  by  the  cables  and  extending 
from  one  tower  to  the  other;  it  is  fastened  to  the  platform  at  the  sev- 
eral points  of  suspension  to  the  cables  and  it  may  be  fastened  to  the 
towers  in  two  ways;  it  maybe  held  in  the  vertical  direction  only, 
anchored  down  as  well  as  supported,  and  acting  as  a  girder  resting  on 
two  supports,  or  it  may  be  fastened  also  in  the  horizontal  direction, 
acting  as  a  girder  fixed  at  the  ends.  The  Board  have  confined  them- 
selves to  the  first  case,  which  has  the  advantage  of  greater  simplicity 
in  computation  of  stresses,  without  material  sacrifice  of  economy. 

The  function  of  a  stiffening  girder  is  to  distribute  a  load  covering 
only  a  part  of  the  span,  over  the  entire  span.  If  this  function  could 
be  performed  without  any  deformation  of  the  girder,  the  distribution 
would  be  perfect  and  the  symmetrical  shape  of  the  cables  would  be 
preserved,  but  as  the  girder  deflects  under  the  load  that  it  carries,  it 
exerts  through  the  suspenders  a  downward  pull  on  the  cables  as  far  as 
the  load  extends,  and  beyond  that  point  the  cable  exerts  a  pull  upward 
on  the  girder.  If  it  is  continuous  it  will  take  the  shape  of  a  reverse 
curve  with  its  point  of  contraflexure  at  the  end  of  the  load.  The  strain 
in  all  the  suspenders  will  be  uniform  for  the  whole  length  of  span.  The 
weight  to  be  carried  by  the  loaded  portion  of  the  stiffening  truss  will 
be  the  moving  load  upon  it,  less  that  carried  by  the  suspenders. 

The  suspenders  over  the  unloaded  portion,  where  the  cable  tends  to 
rise,  are  strained  by  the  resistance  of  the  stiffening  truss  against  flex- 
ure upward.  The  weight  per  unit  of  length  carried  by  the  suspenders 
will  always  be  equal  to  the  live  weight  per  unit  of  length  multiplied 
by  the  length  of  load  and  divided  by  the  length  of  span.  Over  the 
loaded  portion  this  is  the  actual  weight  per  unit  of  length,  less  the  por- 
tion carried  by  the  stiffening  truss.  Over  the  unloaded  portion  this 
represents  the  upward  pull  resisted  by  the  stiffening  truss.  The 
upward  force  per  unit  of  length,  which  tends  to  lift  the  unloaded  por- 
tion, is  therefore  the  assumed  weight  per  unit  of  length  multiplied  by 
the  length  of  load  and  divided  by  the  length  of  span.  The  weight  per 
unit  of  length  carried  by  the  stiffening  truss  on  the  loaded  portion  is 
the  total  weight  per  unit  of  length  less  that  weight  multiplied  by 
length  of  load  and  divided  by  length  of  span. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


45 


When  one-half  of  the  span  is  loaded,  the  weight  will  be  equally 
divided  between  suspenders  and  stiffening  truss;  the  stresses  in  the 
chords  of  the  stiffening  truss  will  be  oue-eiglith  those  caused  by  the 
same  load  extending  over  the  whole  length  of  span  if  the  truss  were 
not  supported  by  suspenders. 

The  greatest  stresses  occur  in  the  continuous  stiffening  truss  when 
either  two-thirds  or  one-third  of  the  span  is  loaded.  In  the  former  case 
the  loaded  portion  must  carry  one-third  of  the  load,  and  the  chord 
stresses  at  the  middle  of  that  two-thirds  will  be  four  twenty-sevenths  of 
the  maximum  stresses  at  center  of  span  if  the  truss  were  fully  loaded 
and  not  supported  by  suspenders;  in  the  latter  case  the  chord  stresses 
at  the  center  of  the  loaded  portion  will  be  only  two  twenty- sevenths, 
while  the  chord  stresses  at  the  center  of  the  unloaded  portion  will  be 
the  four  twenty-sevenths,  but  reversed.  As  the  two-thirds  load  may  be 
placed  anywhere  in  the  truss,  it  follows  that  the  chord  stresses  over 
the  whole  central  third  may  be  four  twenty- sevenths  of  the  maximum 
stress  at  center  of  span  if  the  truss  were  fully  loaded  and  not  supported 
by  suspenders. 

The  shearing  stresses  in  the  webs  of  the  stiffening  truss  are  deter- 
mined by  the  same  distribution  of  loads. 

It  must  be  remembered  that  the  only  stresses  in  the  stiffening  truss 
are  those  due  to  moving  load,  all  dead  weight  being  carried  directly  by 
the  suspenders  to  the  cables. 

While  this  is  the  simplest  explanation  of  the  duties  of  the  stiffening 
truss,  it  does  not  take  into  consideration  all  elements.  The  downward 
and  upward  deflection  of  the  stiffening  truss  must  be  accompanied  by 
corresponding  changes  in  the  shapes  of  the  cables,  but  as  these  changes 
are  in  the  direction  in  which  the  cables  would  move  if  no  stiffening  tr  uss 
existed,  it  follows  that  the  weight  is  not  distributed  equally  among  all 
the  suspenders  and  the  stiffening  truss  is  relieved  of  resisting  so  much 
inequality  as  is  taken  by  the  cables.  The  elongation  of  the  suspenders 
is  also  a  slight  element  of  disturbance,  but  not  sufficient  to  be  described 
here;  an  analysis  of  it  will  be  found  in  Appendix  E. 

There  are  two  other  strains  which  the  chords  of  the  stiffening  truss 
may  be  called  on  to  resist.  The  first  of  these  is  due  to  the  deflection 
of  the  cables  under  temperature  and  under  load.  As  the  stiffening 
truss  is  not  supposed  to  carry  any  of  its  own  weight,  it  must  deflect 
with  the  deflection  of  the  cables,  and  this  deflection  must  be  accom- 
panied by  the  transfer  of  a  portion  of  its  weight  to  itself  with  corre- 
sponding stresses  in  its  chords,  these  chord  strains  being  determined 
entirely  by  the  deflection.  The  other  additional  stress  is  due  to  wind 
pressure  if  the  chords  of  the  stiffening  truss  are  made  the  chords  of 
the  lateral  system,  as  in  ordinary  truss  bridges. 

The  greater  the  depth  of  truss  the  less  the  chord  stresses  due  to  its 
stiffening  duty  and  the  greater  the  stresses  due  to  deflection  of  cables. 
The  wind  stresses  depend  on  the  horizontal  distance  between  the  two 
trusses. 

To  avoid  the  strains  due  to  deflection  of  cables  the  stiffening  truss 
may  be  hinged  at  the  center,  which  can  be  done  by  cutting  one  chord 
and  putting  a  pin  joint  in  the  other.  This  arrangement  fixes  the  point 
of  contrary  flexure  at  the  center  of  the  span  under  all  conditions  of 
loading,  and  leaves  the  stiftening  truss  free  to  rise  and  fall  with  changes 
of  deflection  in  the  cables  without  additional  strain.  As  the  bending 
stresses  at  the  center  are  now  eliminated,  the  only  function  of  the  pin 
joint  will  be  to  transfer  the  shearing  stresses.  With  the  introduction 
of  the  hinge  and  the  fixing  of  the  point  of  contrary  flexure,  the  work 


46 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


of  the  stiffening  trass  is  modified,  and  the  investigation  becomes  more 
complicated;  it  is  given  in  Appendix  E.  The  truss  still  equalizes  the 
weight  on  all  the  suspenders,  but  the  total  weight  carried  by  the  sus- 
penders is  equal  to  the  whole  moving  load  only  when  that  load  covers 
one-halt'  the  span.  The  greatest  chord  stresses  in  either  direction  occur 
at  a  distance  equal  to  0.234  of  the  span  from  each  end,  and  will  be 
0.1500  of  the  maximum  stresses  at  center  of  a  continuous  span  if  the 
truss  were  fully  loaded  and  not  supported  by  suspenders.  The  maxi- 
mum chord  stress  in  the  hinged  truss  is,  therefore,  1.017  times  that  in 
the  continuous  truss,  but  it  is  a  maximum  only  at  two  points  instead 
of  over  one-third  the  span. 

The  continuous  truss  is  better  adapted  to  resist  wind  than  the  hinged 
truss,  but  its  chords  have  to  bear  the  additional  stress  due  to  derlec- 
tion.  As  the  hinged  truss  is  practicable  and  more  economical  than  the 
other,  it  has  been  used  in  the  estimates  made  by  your  Board. 

The  form  which  your  Board  have  selected  for  a  stiffening  truss  is  a 
riveted  lattice  girder  120  feet  deep,  the  two  trusses  being  placed  100 
feet  between  centers.  The  web  members  are  all  inclined  at  an  angle 
of  45  degrees,  and  are  in  eight  systems,  so  that  the  truss  is  divided 
into  30-foot  panels  and  the  unsupported  length  of  each  Aveb  member  is 
about  21  feet.  The  floor  beams  are  hung  from  the  suspenders  and 
carry  the  stiffening  truss,  the  weight  of  which  is  never  entirely  over- 
come by  the  action  of  the  moving  load.  The  top  lateral  system  is  a 
comparatively  light  riveted  lattice.  The  whole  lateral  work  to  resist 
wind  pressure  is  done  by  the  bottom  lateral  system,  in  which  the  floor 
beams  form  lateral  struts  and  .the  diagonals  are  strained  in  tension. 
Cross  bracing  is  provided  at  every  panel  point,  to  sustain  the  floor  beams 
at  their  centers  and  to  transfer  wind  pressure  to  the  bottom  chord,  the 
pull  of  this  cross  bracing  being  resisted  by  the  top  lateral  system. 

Proportioning  the  trusses  for  a  moving  load  of  3,000  pounds  per  foot 
on  each  of  the  six  tracks,  the  maximum  chord  stress  at  the  center  of 
the  half  span  would  be  14,461,400  pounds,  and  the  maximum  chord 
stress  in  the  bottom  chord  at  the  center,  taken  on  the  basis  of  a  wind 
pressure  of  2,000  pounds  per  linear  foot,  would  be  25,000,000  pounds. 
As  the  chords  are  subject  to  reversal  of  strains,  your  Board  have  limited 
the  stresses  in  the  chords  due  to  moving  load  to  12,500  pounds  per 
square  inch  in  each  direction,  making  an  extreme  variation  of  25,000 
pounds,  but  have  allowed  the  stresses  from  the  combined  effects  of 
moving  load  and  wind  to  run  up  to  22,500  pounds,  believing  that,  with 
the  arrangement  of  cradled  cables  hereinafter  described,  the  wind 
strains  will  never  be  anything  like  what  has  been  estimated  on.  They 
have  also  estimated  on  the  chord  sections  never  being  less  than  400 
square  inches.  With  these  conditions,  the  average  section  of  the  bot- 
tom chord  becomes  996  square  inches,  and  that  of  the  top  chord  905 
square  inches,  the  two  averaging  950  square  inches.  Allowing  25  per 
cent  excess  for  details,  the  average  weight  of  each  chord  will  be 
4,037.5  pounds  per  linear  foot. 

The  average  shear  in  the  web  system  will  be  3,000,000  pounds,  in 
addition  to  which  the  web  system  has  to  do  a  duty  in  transferring 
Weight  from  the  upper  to  the  lower  chord  equivalent  to  a  shear  of 
1,300,000  pounds  per  linear  foot,  making  the  total  duty  of  each  web 
equivalent  to  an  average  shear  of  4,300,000  pounds.  If  the  web  is  pro- 
portioned on  the  basis  of  12,500  pounds  per  square  inch,  with  an  allow- 
ance of  50  per  cent  for  details  and  connections,  the  weight  of  each  web 
becomes  3,509  pounds  per  linear  foot. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


47 


The  calculated  weight  of  the  top  laterals  is  500  pounds  per  linear 
foot.  The  calculated  weight  of  the  bottom  laterals,  on  the  basis  of  25,000 
pounds  stress  per  square  inch,  with  an  allowance  of  25  per  cent  for 
details,  is  1,150  pounds  per  linear  foot,  making  a  total  weight  of  later- 
als 1,650  pounds  per  linear  foot. 

The  floor  beams  weigh  90,000  pounds  each,  or  3,000  pounds  per  lin- 
ear foot  of  bridge.  The  stringers  weigh  1,800  pounds  per  linear  foot  of 
bridge.  Floor  beams  and  stringers  are  proportioned  for  a  consolidated 
locomotive  weighing,  with  tender,  104  tous.  The  total  weight  of  the 
suspended  superstructure  per  linear  foot  may  then  be  taken  as  follows: 

Pounds. 


4  chords,  at  4,037.5  pounds   16,150 

2  webs,  at  3,509  pounds   7,018 

Laterals   1,650 

Cross  frames  and  hangers   1,920 

Floor  beams   3,000 

Stringers   1,800 


Total  steel  per  linear  foot  31,538 


This  amounts  to  100,921,600  pounds  for  the  3,200  feet  of  span.  If  to 
this  we  add  2,400  pounds  for  the  weight  of  the  ties  and  rails  and  18,000 
pounds  for  moving  load,  we  have  as  the  total  weight  carried  by  the  sus- 
penders 51,938  pounds  or  26  tons  per  linear  foot. 

This  stiffening  truss  is  a  very  different  structure  from  the  stiffening 
truss  of  any  existing  bridge.  It  is  what  it  purports  to  be,  a  stiffening 
truss,  with  a  heavy  floor  system  like  that  used  in  the  cantilever  design, 
and  with  stiff  connections  throughout.  This  stiffening  truss,  3,200 
feet  long  with  its  floor  system,  weighs  two-fifths  as  much  as  the  entire 
4,320  feet  of  steelwork  of  the  2,000-foot  cantilever  bridge. 

Suspenders. — The  suspenders  would  be  either  wire  ropes  or  cables  of 
straight  wires,  like  the  main  cables.  They  have  been  proportioned  on  the 
basis  of  a  stress  of  30,000  pounds  per  square  inch  of  section,  and  on  this 
basis,  with  an  aflowance  of  20  per  cent  for  connections,  will  weigh  1,425 
pounds  per  linear  foot,  making  the  whole  weight  transferred  to  the 
cables  53,363  pounds.  The  suspenders  weigh  4,560,000  pounds  for  the 
3,200  feet. 

Cables. — The  average  weight  of  the  cables  will  be  14,792  pounds 
per  linear  foot  of  bridge.  The  total  weight  to  be  carried  by  the  cables 
may  therefore  be  taken  at  68,100  pounds  per  linear  foot,  amounting  to 
217,920,000  pounds  or  109,000  tons  for  the  span  of  3,200  feet.  The 
versed  sine  assumed  is  400  feet,  or  one-eighth  of  the  span.  The  great- 
est strain  in  the  cables  will  be  next  to  the  saddles,  and  will  be  equal  to 
the  weight  carried  multiplied  by  1.118,  amounting  to  243,724,000 
pounds,  which,  at  60,000  pounds  per  square  inch,  will  require  4,062 
square  inches.  Six  thousand  No.  3  wires  have  a  total  area  of  316 
square  inches.  The  4,062  square  inches  may  be  divided  into  12  cables 
of  338.5  inches  each.  Your  Board  believe  that  these  cables  can  be  con- 
structed now  as  easily  as  those  of  the  East  River  bridge  were  at  the 
time  it  was  built. 

The  arrangement  of  cables  which  has  seemed  most  feasible  to  your 
Board,  and  which  has  been  used  for  the  basis  of  these  estimates,  places 
six  cables  on  each  side,  the  cables  being  20  feet  apart  on  top  of  towers, 
the  two  cables  next  to  the  center  on  each  side  being  in  vertical  planes, 
and  the  other  cables  cradled  into  planes  which  intersect  in  the  lines  of 
the  pins  which  sustain  the  floor  beams.  A  separate  suspender  reaches 
from  each  pin  to  every  cable,  the  suspenders  being  in  the  same  planes 
as  the  cables.  Vertically  the  cradling  of  the  outside  cables  is  100  feet 
S.  Ex.  1  9 


48 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


in  a  height  of  460  feet,  or  1  in  4.6.  Horizontally  it  is  100  feet  in  a 
total  length  of  3,200  feet,  so  that  the  horizontal  cradling  of  the  two 
outside  cables  is  200  feet  in  3,200  feet,  or  1  in  16.  A  sufficient  cradling 
is  obtained  not  only  to  resist  the  entire  wind  pressure  on  the  cables, 
but  to  relieve  the  lateral  system  very  materially.  The  distance  between 
the  cables  will  favor  simultaneous  construction.  The  suspenders  at 
each  point  will  be  of  uniform  length  and  will  pull  together.  The  length 
of  the  suspenders  at  the  center  of  the  span  must  be  enough  to  allow 
the  cables  to  clear  each  other  where  the  attachment  is  made,  and  this 
places  the  lowest  parts  of  the  cables  60  feet  above  the  pins.  The  total 
height  of  the  towers  above  high  water  is  made  up  as  follows:  Clear- 
ance required  by  law,  150  feet;  camber,  10  feet;  shortest  suspender,  60 
feet;  versed  sine,  400  feet;  total,  620  feet. 

The  total  length  of  each  cable,  from  anchorage  to  anchorage,  is  5,609 
feet.  The  weight  of  each  of  the  12  cables,  per  linear  foot  of  cable, 
including  wrapping,  is  1,183  pounds.  The  weight  of  the  12  cables  is 
14,200  pounds  per  linear  foot,  and  the  total  weight  of  the  cables, 
79,647,800  pounds. 

Towers. — The  weight  transferred  by  the  cables  to  each  tower  is 
218,000  pounds.  The  towers  are  570  feet  high  from  top  of  masonry  to 
saddles.  As  these  towers  are  only  in  compression  and  the  members  so 
large  that  they  may  be  treated  as  short  compression  members,  a  stress 
of  20,000  pounds  per  square  inch  at  the  top  is  permissible.  This 
requires  10,900  square  inches  of  section.  The  weight  of  each  tower 
with  an  allowance  of  80  per  cent  for  details  and  connections  would  be 
38,023,560  pounds  or  76,047,000  pounds  for  both  towers.  The  total 
weight  to  be  carried  on  the  lower  part  of  the  tower  would  be  128,000 
tons,  making  a  pressure  of  less  than  24,000  pounds  per  square  inch  at 
the  base  of  the  steel  columns,  which  will  be  very  slightly  increased  by 
the  wind  pressure  and  by  the  horizontal  deflections  at  the  top  of  the 
towers  if  the  saddles  do  not  move  freely. 

Anchor  chains. — The  cables  are  carried  in  straight  lines  from  the 
saddles  to  the  anchorages,  each  anchorage  being  in  two  parts,  each 
part  anchoring  the  six  cables  on  its  side  of  the  bridge.  The  upward 
pull  of  the  cables  at  each  anchorage  (one  side)  is  54,500,000  pounds 
and  the  horizontal  pull  109,000,000  pounds.  The  estimates  have  been 
made  on  the  basis  of  connecting  the  cables  with  the  anchor  bars  out- 
side of  the  masonry  of  the  anchorage,  placing  these  anchor  bars  in  tun- 
nels, and  connecting  them  with  bearing  plates  at  the  lower  end;  every- 
thing would  be  accessible  for  care  and  repairs.  The  chains  would  be 
of  steel  eyebars  which  have  been  proportioned  for  a  stress  of  20,000 
pounds  per  square  inch  with  an  allowance  of  20  per  cent  for  details. 
The  estimated  weight  of  the  bars  and  pins  in  each  of  the  four  half 
anchorages  is  6,825,000  pounds,  while  the  plates  at  the  bottom  would 
add  600,000  pounds  to  this  amount,  making  the  total  weight  in  each 
half  anchorage  7,425,000  pounds,  or  29,700,000  pounds  in  the  four. 

Structural  steel. — In  estimating  the  cost  of  the  structural  steel  work, 
your  Board  have  used  the  same  price  per  pound  as  for  the  work  in  the 
cantilever  bridge,  namely,  4£  cents.  On  this  basis  the  cost  would  be  as 
follows  : 


Pounds. 


Suspended  superstructure 

Towers  

Chains  

Anchor  plates  


100,  921, 600 
76,  047, 000 
27,  300.  000 
2,  400,  000 


Structural  steel 


206,  668,  600,  at  4£  cents,  $9,300,087. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


49 


Tlie  majority  of  the  Board  believe  that  this  price  is  too  high,  owiug 
to  the  difference  in  character  of  steel  work  in  the  two  structures,  and 
that  the  total  cost  of  the  structural  steel  work  should  not  be  estimated 
higher  than  $8,500,000. 

Wireworlc. — The  cables  and  suspenders  have  been  estimated  at  8 
cents  per  pound,  making  their  cost — 


Pounds. 

Cables   79,  647,  800 

Suspenders   4,560,000 


Total  wire   84.  207,  800,  at  8  cents,  $6,736,624. 


Superstructure. — The  total  cost  of  the  superstructure  is  $10,030,711, 
on  the  basis  of  4J  cents  for  all  structural  steel. 

Substructure. — The  substructure  would  consist  of  two  anchorages  and 
the  bases  for  two  towers.    Each  tower  base  has  to  carry  the  following 


weights : 

Tons. 

Suspended  weight  on  top  of  tower   109,  000 

Tower   19,  000 

Extra  effect  of  wind   4,  000 


Total   132,  000 


Each  of  the  tower  bases  of  the  2,000-foot  cantilever  bridge  carries 
100,000  tons.  In  both  cases  the  foundations  can  be  made  proportional 
to  the  weights  carried. 

The  east  tower  is  in  the  same  place  as  the  east  pier  of  the  canti- 
lever bridge.  The  cost  of  this  base  for  the  suspension-bridge  tower 
will  be  that  of  the  cantilever-bridge  pier,  or  $3,464,000,  multiplied  by 
1.32,  making  $4,572,480. 

The  west  tower  would  come  immediately  west  of  the  New  Jersey 
pier-head  line,  the  average  depth  of  rock  being  about  10  feet  more 
than  on  the  east* side,  requiring  414,000  cubic  feet  additional  in  the 
foundation.  Estimating  on  the  same  basis  as  for  the  west  pier  of  the 
cantilever  bridge,  the  cost  of  this  414,000  cubic  feet  of  foundation 
would  be  $431,000,  which  would  make  the  cost  of  the  west  tower  base 
$5,003,480. 

The  anchorages  have  been  planned  on  the  basis  of  putting  the  entire 
weight  which  is  to  resist  the  pull  of  the  cables  above  mean  high  water, 
and  the  quantities  have  been  based  on  a  coefficient  of  friction  of  0.6 
and  a  factor  of  safety  of  2.  The  anchorage  at  each  end  of  the  bridge 
would  contain  5,940,000  cubic  feet  above  the  foundation.  The  only 
duty  of  the  anchorages  is  to  act  as  weight,  and  a  very  cheap  class  of 
masonry  can  be  used  for  this  purpose;  rubble  made  of  the  most  avail- 
able stone,  with  a  faciug  of  rough  ashlar  or  brick,  would  do.  The  cost 
of  this  masonry  has  been  estimated  at  37 \  cents  per  cubic  foot,  although 
the  Board  believe  it  could  be  built  for  much  less.  On  this  basis  the 
cost  of  each  auchorage  above  mean  high  water  is  $2,227,500. 

The  east  anchorage  would  be  founded  where  the  rock  is  20  feet  below 
mean  high  water ;  the  foundation  could  be  put  in  with  an  open  coffer- 
dam, and  has  been  estimated  as  costing  75  cents  per  cubic  foot.  There 
would  be  1,150,000  cubic  feet  in  this  foundation,  making  the  cost  $862,500, 
and  the  total  cost  of  the  east  anchorage  $3,090,000. 

The  foundation  of  the  west  anchorage  would  have  to  be  sunk  60  feet 
to  reach  the  rock,  and  would  probably  be  put  in  by  the  pneumatic 
process.  Its  volume  would  be  three  times  that  of  the  east  anchorage, 
and  its  cost  may  be  estimated  at  the  same  price  per  cubic  foot,  or 
$2,587,500,  making  the  total  cost  of  the  west  anchorage  $4,815,000. 
S.  E.  12  4 


50 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  total  cost  of  the  substructure  would  then  be: 

East  anchorage   $3,  090,  000 

Base  for  east  tower   4,  572,  480 

Base  for  west  tower   5,  003,  480 

West  anchorage   4,  815,  000 

Substructure   17,480,960 

The  anchorages  can  be  adapted  to  carry  the  tracks,  but  the  tracks 
must  be  carried  between  them  and  the  towers  on  viaducts,  requiring 
925  feet  of  viaduct  on  each  side,  or  1,850  feet  in  all,  which  has  been 
estimated  at  the  same  price  as  before.  The  total  length  of  the  suspen- 
sion bridge,  including  viaducts  and  anchorages,  is  5,600  feet.  The  total 
cost  will  be  as  follows : 

Superstructure   $16,  036,  711 

Substructure   17,  480,  960 

33,  517,  671 

Viaduct   1,  850,  000 

Total   35,367,671 

The  estimated  cost  of  the  2,000-foot  cantilever  bridge  was  $25,443,000 
for  4,320  feet;  to  compare  it  with  the  5,600-foot  suspension  bridge,  1,280 
feet  of  viaduct  must  be  added;  this  makes  the  cost  $26,723,000;  the  esti- 
mated cost  of  the  suspension  bridge  is  $8,644,671  more.  The  fairest 
comparison  is  by  percentages;  the  cost  of  the  suspension  bridge  is 
nearly  32J  per  cent  more  than  that  of  the  2,000-foot  cantilever  bridge. 
If  allowance  is  made  for  cost  oi  structural  steel  in  accordance  with  the 
views  of  a  majority  of  the  Board,  the  difference  will  be  reduced  to 
$7,844,584,  or  nearly  30  per  cent.  The  general  conclusion  vhich  your 
Board  have  reached  is  that  the  cost  of  a  suspension  bridge  of  a  single 
span,  designed  for  its  whole  length  for  the  same  moving  load  as  the 
2,000-foot  cantilever  bridge,  would  be  less  than  one-third  more  than  that 
of  the  cantilever. 

Deflections. — The  structure  described  is  one  of  unusual  rigidity.  The 
expansion  of  the  metallic  towers  counteracts  in  a  degree  deflections 
due  to  elongation  of  cables  under  an  increase  of  temperature,  this 
deflection  being  further  reduced  by  the  large  versed  sine.  Of  the  34 
tons  per  linear  foot,  only  9  are  moving  load,  so  that  the  stress  per  square 
inch  on  cables  caused  by  a  maximum  moving  load  is  less  than  16,000 
pounds ;  it  would  not  exceed  5,000  pounds  with  an  ordinary  freight 
train  on  every  track,  or  2,500  pounds  with  a  passenger  train  on  every 
track.  The  deflections  have  been  calculated  for  a  full  moving  load 
with  the  following  results: 


Conditions. 


60  degrees  ±  F  

Maximum  mov.  load 

Combined  


Effects  of— 

Cable 
between 
towers. 

Back 
stays. 

Towers. 

Sus- 
penders. 1 

+  2 

-2.  75 

+  0.1 
-0. 14 

±0. 22 
-0.11 

+  0.03  1 
-0.02  | 

-,75 

-0.  24 

+  0.  11 

-0.05  | 

Total. 


+■1.91 
-3.02 


In  other  words,  the  total  deflection  at  the  center  of  the  span  below  a 
mean  is  about  5  feet;  the  deflection  above  a  mean  is  less  than  2  feet; 
the  total  range  is  less  than  7.  These  deflections  are  within  satisfactory 
limits  for  railroad  service. 

A  deflection  of  5  feet  in  a  length  of  3,200  feet,  calculated  for  a  modu- 
lus of  elasticity  of  28,000,000  pounds,  corresponds  to  a  chord  stress  of 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


51 


7,870  pounds  per  square  inch  in  a  stiffening  truss  120  feet  deep.  This 
is  the  stress  which  has  been  eliminated  by  the  use  ef  the  hinge. 


The  calculations  of  the  cost  of  the  suspension  bridge  which  has  been 
described  have  been  made  as  nearly  as  possible  on  the  same  basis  as 
the  estimates  for  the  cantilever  bridge,  without  taking  into  consider- 
ation the  fact  that  the  cantilever  bridge  would  be  strained  nearly  to 
its  full  capacity  by  a  load  1,000  feet  long,  while  the  suspension  bridge 
would  be  fully  strained  only  when  covered  by  a  load  three  times  that 
length.  Furthermore,  no  allowance  has  been  made  for  the  fact  that 
the  maximum  strains  in  the  stiffening  truss  would  occur  only  under 
combinations  which  might  not  arise  once  in  a  century,  and  which  could 
be  prevented  by  simple  police  regulations. 

A  moving  load  of  3,000  pounds  per  foot,  1,000  feet  long,  on  each  of 
the  0  tracks,  crossing  the  bridge  without  change  of  relative  position, 
would  produce  practically  maximum  effects  in  upward  moments  on  a 
continuous  stiffening  truss,  but  it  would  produce  only  one-half  these 
moments  downward.  In  other  words,  the  chords  of  the  stiffening 
truss  would  be  strained  12,500  pounds  per  square  inch  by  upward 
bending,  but  only  6,250  pounds  by  downward  bending,  on  the  assump- 
tion as  before  that  all  the  moving  load  is  distributed  by  the  stiffening 
truss;  as  only  about  88  per  cent  is  distributed  by  reason  of  the 
unsymmetrical  deflection  of  the  cable,  the  maximum  chord  stresses  are 
reduced  and  become,  respectively,  11,000  and  5,500  pounds.  The  great- 
est upward  deflection  from  the  action  of  the  cables  occurs  from  the 
effects  of  temperature  when  the  bridge  is  unloaded;  under  a  full  load 
it  is  eliminated,  and  under  a  1,000-foot  load  it  is  reduced  to  about  1  foot, 
which  corresponds  to  a  chord  stress  of  1,570  pounds,  making  a  total  of 
12.570.  The  downward  deflection  would  never  exceed  3J  feet  with 
the  limited  leng^i  of  train,  which  corresponds  to  a  chord  strain  of 
5,509  pounds,  or  a  total  of  11,099,  so  that  a  continuous  truss  could  be 
used  without  exceeding  the  assumed  limits  of  stress.  It  should  be 
noted  that  the  only  condition  which  would  produce  these  stresses  would 
be  the  passage  of  six  maximum  trains  side  by  side.  A  single  freight 
train  in  the  most  unfavorable  position  would  produce  a  stress  of  not 
over  3,500  pounds  in  the  chords  of  the  stiffening  truss,  and  a  single 
passenger  train  a  stress  of  not  over  1,800  pounds.  In  providing  for  a 
lighter  structure  adapted  to  trains  1,000  feet  long,  it  has  been  thought 
best  to  make  no  reduction  in  the  weight  of  the  stiffening  truss  or  the 
floor  system,  but  the  continuous  form  of  truss  might  be  selected. 

If  the  stiffening  truss  did  its  complete  duty  in  the  distribution  of 
weight,  the  greatest  strain  which  a  train  1,000  feet  long,  weighing  3,000 
pounds  per  foot,  could  throw  upon  the  cables,  would  correspond  to  a 
uniform  load  of  937  pounds.  If  the  stiffening  truss  did  no  duty  what- 
ever, but  the  weight  was  distributed  strictly  according  to  the  laws  of 
leverage,  the  greatest  strain  which  such  1,000-foot  train  could  throw 
upon  the  cables  would  correspond  to  a  uniform  load  of  1.582  pounds 
per  linear  foot.  Under  these  circumstances  it  seems  safe,  while  not 
reducing  the  stiffening  truss,  to  provide  for  a  moving  load  on  the  cables 
of  only  1,500  pounds  per  foot  of  track.  For  this  approximate  calcula- 
tion, the  weights  per  linear  foot  may  then  be  taken  as  follows: 


LIGHTER  STRUCTURE. 


Suspended  superstructure  and  tracks 

Moving  load  , 

Cables  and  suspenders  


Pounds-. 
34.  000 

!•.  «  Mil) 

14.  000 


Total 


57,  000 


52 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


This  is  28 J  tons  per  linear  foot,  instead  of  34  tons,  the  reduction  in 
the  total  carrying  capacity  being  about  16  per  cent.  It  should  be 
observed  that  the  live  load  is  only  15.8  per  cent  of  the  whole,  so  that 
the  additional  stress  put  on  the  cables  by  the  simultaneous  passage  of 
six  maximum  trains  would,  without  allowance  for  the  work  of  the  stif- 
fening truss,  be  only  10,000  pounds  per  square  inch.  The  stress  imposed 
by  a  1,000-foot  passenger  train  under  the  most  unfavorable  conditions 
would  not  be  over  1,200  pounds. 

For  purposes  of  the  present  comparison,  the  suspended  superstructure 
remains  unchanged;  all  other  parts  may  be  taken  at  16  per  cent  less 
than  in  the  previous  estimate.  The  weights  and  cost  of  such  a  bridge 
may  then  be  estimated  as  follows : 

Pounds. 

Suspended  superstructure   101,000,000 

Towers   64,  000,  000 

Chains  and  anchor  plates   25,  000,  000 

Structural  steel   190,000,000,  4£  cents.. .  $8,550,000 

Wire  work   5,659,000 

Total  superstructure   14,  209,  000 

Substructure   14,684,000 

28,  893,  000 

Add  for  viaduct   1,  850,  000 

30,  743,  000 

This  is  $4,625,000  less  than  the  previous  estimate,  aiid  $4,020,000,  or 
about  15  per  cent,  more  than  the  cost  of  the  cantilever  with  the  2,000- 
foot  clear  span. 

This  estimate  has  been  made  for  the  purpose  of  comparing  on  the 
same  basis,  that  of  a  factor  of  safety  of  three  on  ultimate  strength  of 
metal,  the  2,000-foot  cantilever  and  the  suspension  bridge  ^hen  carry- 
ing train  loads  1,000  feet  long.  If  it  be  thought  that  the  stress  of 
60,000  pounds  per  square  inch  on  the  wire  in  the  cables  is  too  high,  it 
may  be  noted  that  the  difference  in  the  cost  of  wirework  in  the  two 
suspension  bridge  estimates  is  $1,017,624,  and  if  the  higher  cost  is 
restored  it  will  be  equivalent  to  reducing  the  stress  in  wire  to  about 
50,000  pounds  per  square  inch.  With  this  change  the  cost  of  the 
lighter  structure  becomes  $31,671,000,  this  being  $5,038,000,  or  about 
19  per  cent,  more  than  that  of  the  2,000-foot  cantilever. 

If  only  one  train  is  allowed  on  one  track  at  a  time,  maximum  stresses 
will  occur  in  the  different  members  no  oftener  than  the  same  loads 
would  produce  maximum  stresses  in  the  2,000-foot  cantilever.  More- 
over, the  load  of  1,500  pounds  per  foot  adopted  for  the  cables  is  the 
full  weight  of  a  passenger  train  and  would  not  be  exceeded  if  the  entire 
span  were  covered  with  the  heaviest  class  of  passenger  equipment. 


UPPER  LOCATION. 


If  a  location  near  Sixty-ninth  street  were  adopted,  the  conditions 
would  be  a  little  more  unfavorable  for  the  foundations  of  the  towers, 
but  very  much  more  favorable  for  the  anchorages,  as  rock  is  found 
above  water  on  both  sides.  The  cost  of  the  two  anchorage  foundations 
is  $3,450,000  in  the  first  estimate  and  $2,900,000  in  the  second  estimate; 
these  foundations  would  be  saved  at  the  upper  location.  These  figures 
are  enough  to  show  that  there  are  points  within  the  limits  prescribed 
by  the  act  where  the  difference  in  cost  between  the  2.000-foot  canti- 
lever and  the  single-span  suspension  bridge  might  be  much  less  than 
has  been  estimated. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


53 


CONCLUSION. 

The  only  subject  referred  to  your  Board  is  to  "recommend  what 
length  of  span  not  less  than  2,000  feet  would  be  safe  and  practicable 
for  a  railroad  bridge  to  be  constructed  over"  the  Hudson  River  between 
Fifty-ninth  and  Sixty-ninth  streets.  A  single  span  from  pier  head  to 
pier  head,  built  on  either  the  cantilever  or  suspension  x^rineiple,  would 
be  safe.  The  estimated  cost  of  the  3,100-foot  clear-span  cantilever 
being  about  twice  that  of  the  shorter  span,  your  Board  consider  them- 
selves justified  in  pronouncing  it  impracticable  on  financial  grounds. 
As  the  cost  of  the  single-span  suspension  bridge  is  at  most  one  third 
greater  than  that  of  the  2,000-foot  cantilever,  your  Board  are  unable  to 
say  that  such  greater  cost  is  enough  to  render  the  suspension  bridge 
impracticable. 

The  Board  have  reached  this  conclusion  after  careful  study,  and  they 
have  thought  it  best  to  give  the  full  course  of  reasoning  which  they 
have  followed.  They  feel  that  the  contingency  attending  the  construc- 
tion of  the  deep  river  foundation  of  the  cantilever  bridge,  even  waiving 
the  absolute  necessity  of  carrying  this  foundation  to  rock,  is  enough  to 
balance  a  part  of  the  greater  cost  of  the  suspension  bridge. 

The  conclusion  of  this  Board  is  that  of  a  Board  of  Bridge  Engineers 
acting  in  a  professional  capacity.  While  from  such  professional  view 
they  must  pronounce  the  suspension  bridge  practicable,  they  do  not  in 
this  conclusion  give  an  opinion  on  the  financial  practicability  and  merit 
of  either  plan. 

Before  closing,  your  Board  desire  to  state  particularly  that  the  esti- 
mates have  been  made  for  comparative  purposes  and  are  not  to  be 
taken  as  a  measure  of  absolute  cost ;  they  are  believed  to  be  thoroughly 
fair  for  comparisons ;  the  prices  assumed  may  be  much  higher  than 
absolute  cost.  The  plans  on  which  the  estimates  are  made,  a  sketch  of 
which  accompanies  this  report,  would  undoubtedly  be  modified  if  a 
bridge  were  buijt. 

This  report  is  accompanied  by  the  following  appendices: 

A.  — Act  approved  June  1,  1894. 

B.  — Statement  prepared  by  Mr.  Charles  Macdonald  in  behalf  of  the  New  York  and 

New  Jersey  Bridge  companies.    (Six  inclosures,  including  four  blue  prints.) 
C— Statements  of  Mr.  Gustav  H.  Schwab  (C)  and  Win,  W.  Hildenbrand  (C1  —  C2). 
(Two  inclosures,  tracings.) 

D.  — Statement  of  Mr.  G.  Lindenthal. 

E.  — Theoretical  investigation  of  stiffening  truss. 

Respectfully  submitted. 

G.  BOTJSCAREN. 

W.  H.  Burr. 
Theodore  Cooper. 
Geo.  8.  Morison. 
0.  W.  Raymond. 

Hon.  Daniel  S.  Lamont, 

Secretary  of  War. 

INDORSEMENT  OF  SECRETARY  OF  WAR  ON  THE  FOREGOING  REPORT. 

War  Department, 

December  12,  1894. 
The  Board  having  reported  that  a  single  span  from  pier -head  to 
pier-head  would  be  safe  and  not  impracticable,  I  approve  such  report 
and  plans  may  be  submitted  for  a  bridge  with  a  single  span  from  pier- 
head to  pier-head. 

Daniel  S.  Lamont, 

Secretary  of  War. 


54 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


Appendix  A. 

ACT  APPROVED  JUNE  7,  1894. 

[Public— No.  83.] 

AN  ACT  To  authorize  the  New  York  and  New  Jersey  Bridge  Companies  to  construct  and  maintain  a 
bridge  across  the  Hudson  River  between  New^York  City  and  the  State  of  New  Jersey. 

Be  it  enacted  by  the  Senate  and  House  of  Representatives  of  the  United  States  of  America 
in  Congress  assembled,  That  the  New  York  and  New  Jersey  Bridge  Companies,  here- 
tofore incorporated  by  the  States  of  New  York  and  New  Jersey,  and  existing  under 
the  laws  of  said  States,  are  hereby  authorized  to  construct,  operate,  maintain,  and 
rebuild,  in  case  of  destruction,  a  bridge  across  the  Hudson  River  between  New  York 
City,  in  the  county  and  State  of  New  York,  and  the  State  of  New  Jersey,  subject  to 
the  laws  of  said  States,  respectively,  upon  the  following  terms,  limitations,  and 
conditions : 

First.  That  the  location  of  said  bridge  shall  be  subject  to  approval  by  the  Secre- 
tary of  War,  upon  such  examinations,  hearings,  and  reports  as  he  shall  hereafter 
prescribe:  Provided,  That  it  shall  not  be  located  below  Fifty-ninth  street,  New  York 
City,  nor  above  Sixty-ninth  street,  New  York  City. 

Second.  That  the  said  companies  may  locate,  construct,  and  maintain  over  such 
bridge  and  the  approaches  thereto  railroad  tracks  for  the  use  of  railroads :  Provided, 
That  any  railroad  on  either  side  of  said  river  shall  be  permitted  to  connect  its  tracks 
with  the  said  bridge  approaches,  and  shall  have  equal  rights  of  transit  for  its  rolling 
stock,  cars,  passengers,  and  freight  upon  equal  and  equitable  terms,  and  if  a  dispute 
as  to  the  equality  or  equity  of  the  terms  shall  arise  it  shall  be  submitted  to  and 
decided  by  the  Secretary  of  War:  Provided,  That  the  location  of  all  approaches  of 
said  bridge  in  the  city  of  New  York  shall  be  approved  by  the  commissioners  of  the 
sinking  fund  of  the  city  of  New  York  :  And  provided  f  urther,  That  no  railroad  or  rail- 
roads shall  be  operated  on  the  approaches  of  said  bridge  companies  in  the  city  of 
New  York,  except  on  such  approaches  as  shall  have  been  approved  by  the  sinking- 
fund  commissioners  of  the  city  of  New  York :  Provided,  also,  That  the  term  approaches 
as  used  in  this  Act  shall  be  construed  to  include  only  such  portion  of  the  roadbed 
and  superstructure,  on  either  side  of  said  bridge,  as  is  necessary  to  reach  the  grade 
of  the  bridge  from  the  grade  of  the  streets  at  which  said  approaches  begin  to  rise, 
in  order  to  bring  the  two  elevations  together  upon  and  by  a  grade  of  not  less  than 
twenty  feet  to  the  mile. 

Third.  That  any  bridge  built  under  the  authority  of  this  Act  shall  be  constructed 
with  such  length  of  span  and  at  such  elevation  as  the  Secretary  of  War  shall  approve 
and  require:  Provided,  however,  That  it  shall  afford,  under  any  conditions  of  load  or 
temperature,  a  minimum  clear  headway  above  high  water  of  spring  tides  of  not 
less  than  one  hundred  and  fifty  feet  at  the  center  of  the  span;  and.  all  the  plans  and 
specifications,  with  the  necessary  drawings  of  said  bridge,  shall  be  submitted  to  the 
Secretary  of  War  for  his  approval,  and  before  such  approval  the  construction  shall 
not  be  begun ;  and  should  any  change  be  made  in  said,  plans  during  progress  of  con- 
struction, such  changed  plans  shall  be  submitted  to  said  Secretary  and  approved 
by  him  before  made;  and  the  President  shall  appoint  a  board,  consisting  of  five 
competent,  disinterested,  expert  bridge  engineers,  of  whom  one  shall  be  either  the 
Chief  of  Engineers  or  any  member  of  the  Corps  of  Engineers  of  the  United  States 
Army,  and  the  others  from  civil  life,  who  shall,  within  thirty  days  after  their 
appointment,  meet  together  and,  after  examination  of  the  question,  shall,  within 
sixty  days  after  their  first  meeting,  recommend  what  length  of  span,  not  less  than 
two  thousand,  feet,  would  be  safe  and  practicable  for  a  railroad  bridge  to  be  con- 
structed over  said  river,  and  file  such  recommendation  with  the  Secretary  of  War, 
but  it  shall  not  be  final  or  conclusive  until  it  has  received  his  written  approval.  In 
case  any  vacancy  shall  occur  in  said  board,  the  President  shall  fill  the  same.  The 
compensation  and  expenses  of  said  board  of  engineers  shall  bo  fixed  by  the  Secretary 
of  War  and  paid  by  the  said  bridge  companies,  which  said  companies  shall  deposit  with 
the  Secretary  of  War  such  sum  of  money  as  he  may  designate  and  require  for  such 
purpose:  Provided,  always,  That  nothing  herein  contained  shall  be  construed  as  pre- 
venting the  said  board  of  engineers  from  meeting,  investigating,  and  filing  their 
recommendation  after  the  expiration  of  said  time  herein  mentioned. 

Fourth.  The  companies  oj^erating  under  this  law  shall  maintain  on  the  bridge,  at 
their  own  expense,  from  sunset  to  sunrise,  such  lights  and  signals  as  the  United 
States  Light-House  Board  may  prescribe. 

Fifth..  The  said  company  or  companies  availing  themselves  of  the  privileges  of 
this  Act  shall  not  charge  a  higher  rate  of  toll  than  authorized  by  the  laws  of  the 
State  of  New  York  or  New  Jersey,  and  the  mails  and  troops  of  the  United  States 
shall  be  transported  free  of  charge  over  said  bridge. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


55 


Sixth.  That  said  company  or  companies  shall  he  subject  to  the  interstate-com- 
merce law,  and  to  all  amendments  thereof,  and  when  such  bridge  is  constructed 
under  the  provisions  of  this  Act  it  shall  he  a  lawful  military  and  post  road  and  a 
lawful  structure. 

Seventh.  That  the  said  company  or  companies  availing  themselves  of  the  privileges 
of  this  Act  shall  file  an  acceptance  of  its  terms  with  the  Secretary  of  War,  and  shall 
submit  to  the  Secretary  of  War,  within  one  year  after  the  passage  of  this  Act,  for 
examination  and  approval,  drawings  showing  plan  and  location  of  the  bridge  and  its 
approaches;  and  the  construction  of  said  bridge  shall  be  commenced  within  one 
year  after  said  location  and  plans  have  been  approved  of,  as  herein  provided ;  and 
said  company  or  companies  shall  expend,  within  the  first  year  after  construction  has 
commenced,  as  herein  required,  not  less  than  two  hundred  and  fifty  thousand  dollars 
in  money,  and  in  each  year  thereafter  not  less  than  one  million  of  dollars  in  money  in 
the  actual  construction  work  of  said  bridge,  which  shall  be  reported  to  the  Secretary 
of  War;  and  the  said  bridge  shall  be  completed  within  ten  years  from  the  commence- 
ment of  the  construction  of  the  same,  as  herein  required;  and,  unless  the  actual  con- 
struction of  said  bridge  shall  be  commenced,  proceeded  with,  and  completed  within 
the  time  and  according  to  the  provisions  herein  provided,  this  Act  shall  be  null  and 
void. 

The  right  to  amend,  alter,  modify,  or  repeal  this  Act  is  hereby  reserved. 
Approved,  June  7,  1894. 


Appendix  B. 

STATEMENT  OF  MR.  CHARLES  MACDONALD,  OF  UNION  BRIDGE  COMPANY. 

No.  1  Broadway,  New  York,  July  20, 1894. 

Sir:  In  accordance  with  your  permission,  I  have  the  honor  to  submit  herewith 
certain  general  information  relating  to  the  proposed  bridge  across  the  Hudson 
River,  authorized  by  recent  act  of  Congress,  and  under  which  act  your  Board  has 
also  been  constituted. 

The  bridge  in  question  must  be  located  between  Fifty-ninth  and  Sixty-ninth  streets 
and  your  Board  is  to  advise  as  to  what  is  a  safe  and  practicable  span,  not  less  than 
2,000  feet,  for  such  a  location. 

The  New  York  and  New  Jersey  Bridge  Company  has  in  view  the  construction  of  a 
bridge  for  utilitarian  purposes  only.  There  is  to  be  nothing  of  the  monumental  or 
sentimental  character  about  it,  except  in  so  far  as  must  be  inseparably  connected 
with  its  magnitude.  It  is  intended  to  build  a  structure  which  will  safely  provide 
facilities  for  all  the  traffic  which  may  be  expected  to  pass  over  it,  as  well  as  under 
it,  and  at  such  practicable  cost  as  will  prove  attractive  to  the  investors  of  capital. 
It  is  not  committed  to  any  particular  design  of  bridge,  whether  it  be  cantilever,  sus- 
pension, or  a  combination  of  the  two.  What  it  intends  to  build,  if  permitted  to  do 
so,  is  a  structure  which  will  accomplish  the  desired  results  with  the  least  expendi- 
ture of  money. 

The  first  element  in  this  problem  is,  necessarily,  the  determination  of  the  proba- 
ble traffic.  From  a  careful  observation  of  the  number  of  cars  arriving  at  Jersey 
City,  the  amount  of  express  freight,  and  the  number  of  passengers  which  would  be 
likely  to  pass  over  the  bridge,  it  has  found  that  the  gross  income  (from  all  sources) 
will  not  exceed  $3,500,000,  that  the  cost  of  maintenance,  taxes,  etc.,  would  be 
$1,250,000,  leaving  as  available  for  paymeut  of  interest,  after  deducting  all  other 
charges,  $2,250,000.  This,  at  5  per  cent,  represents  a  total  investment  of  $45,000,000. 
Of  this  amount  about  one-half  will  be  required  for  terminals  (including  right  of 
way). 

Thus  it  would  appear  that  if  the  bridge  proper  can  be  built  at  a  cost  of  $22,500,000 
the  entire  investment  might  possibly  be  favorably  considered.  Our  efforts  have, 
therefore,  been  confined  within  this  iiniit  of  cost,  and  the  results  are  respectfully 
presented  for  your  consideration. 

It  is  proposed  to  build  a  "cantilever"  bridge,  having  a  span  of  2,300  feet  between 
centers  ot  main  towers,  or  upward  of  2,000  feet  in  the  clear,  and  2  anchor  spans  of 
910  ieet  each  between  center  of  main  tower  and  anchorage  pier. 

The  clear  height  above  high  water,  at  center  of  main  span,  will  be  150  feet. 

There  will  be  6  railway  tracks  throughout  the  entire  length  of  bridge  and 
approaches. 

The  main  towers  will  rest  upon  4  cylinders,  each  arranged  in  the  form  of  a  square, 
of  200  feet  between  centers.  They  will  finish  off  with  granite  masonry  at  a  height 
of  25  feet  above  high  water. 

The  anchorage  piers  will  be  founded  upon  cylinders  and  finished  off  with  granite 
masonry  to  the  underside  of  the  bottom  chord  of  the  trusses. 


56 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


In  accordance  with  the  law  of  the  State  of  New  York  upon  which  the  charter  is 
based,  the  main  tower  on  the  New  York  side  is  placed  wholly  within  the  pierhead 
line.  The  anchorage  pier  on  the  New  Jersey  side  is  placed  wholly  within  the  pier- 
head line  on  that  side  of  the  river,  and  the  center  of  the  river  pier  is  about  JJOO  feet 
eastward  from  this  same  line. 

Accurate  borings  have  been  made  at  different  points  within  the  limits  of  location 
permitted  by  the  act,  from  which  it  appears  that  the  distance  from  high  water  to 
rock  or  bowlder  (at  the  site  of  the  river  pier)  is  upward  ef  250  feet,  while  sand  is 
found  at  a  depth  of  165  feet. 

It  is  proposed  to  construct  this  river  pier  on  a  sand  foundation,  at  a  depth  of  200 
feet  below  low  water.  The  diagram  submitted  herewith  indicates  the  general 
dimensions  and  pressures  for  each  of  the  4  cylinders  composing  this  foundation. 

The  cylinders  under  the  New  York  pier  would  be  of  the  same  dimensions,  but  the 
depth  to  a  suitable  sand  foundation  would  be  somewhat  less. 

Detailed  strain  sheets  are  herewith  submitted,  showing  the  general  distribution 
of  material  required  to  insure  safety  for  the  live  load  on  six  tracks  having  an  average 
of  3,000  pounds  per  running  foot  on  each  track. 

Suitable  provision  has  also  been  made  for  wind  strains  and  for  strains  during 
erection  wherever  they  exceed  normal  strains. 

It  will  be  observed,  by  reference  to  the  diagram  of  the  foundation  cylinder,  that 
the  total  pressure  (from  live  and  dead  loads  and  wind  strains)  upon  the  top  of  the 
granite  capping  is  8.84  tons  per  square  foot,  and  that  the  abnormal  pressure  on  the 
base,  where  the  concrete  filling  comes  into  contact  with  the  sand  (at  a  depth  of  200 
feet),  is  7.16  tons  per  square  foot. 

The  nearest  precedent  believed  to  be  in  existence  for  a  deep  foundation  of  this 
character  is  the  pier  foundation  for  the  Hawkesbury  bridge  in  New  South  AVales,  a 
diagram  of  which  is  herewith  submitted.  The  abnormal  pressure  per  square  foot  in 
this  latter  case  is  5.7  tons,  with  a  depth  of  only  8  feet  in  the  sand,  and  at  a  total 
depth  of  162  feet  below  high  water. 

As  it  is  well  known  that  the  resisting  force  increases  with  the  depth,  it  is  believed 
that  the  assumption  herein  taken  is  justifiable,  but  in  order  to  make  sure  it  is  pro- 
posed (and  provision  has  been  made  in  the  estimate  for  same)  to  sink  a  trial  cylin- 
der, 20  feet  diameter,  in  the  center  of  the  square  between  the  four  cylinders  com- 
posing the  river  pier.  From  the  experimental  data  thus  obtained  as  to  the  exact 
amount  of  skin  friction  and  resistance  to  settlement,  more  accurate  proportions  can 
be  given  to  the  main  cylinders,  particularly  with  reference  to  the  relation  of  weight 
required  to  cause  settlement  during  dredging. 

It  will  be  observed  that  the  effect  of  skin  friction  has  not  been  considered  in  cal- 
culating the  supporting  value  of  the  foundations.  This  will  be  wholly  on  the  side 
of  safety,  therefore,  and  will  unquestionably  reduce  the  abnormal  pressure  on  the 
sand  at  the  foot  of  the  cylinder. 

These  cylinders  will  be  filled  up  with  concrete  made  of  the  best  Portland  cement, 
lowered  through  the  water  in  the  most  approved  manner,  and  finished  off  at  about 
the  level  of  the  bottom  of  the  river.  The  outer  skin  of  the  cylinder  will  be  carried 
up  above  high  water,  temporarily,  to  facilitate  the  construction  of  the  masonry  from 
the  river  bottom  upward. 

In  the  completed  pier  there  will  be  no  metal  work  exposed  to  corrosion  where  it 
might  give  rise  to  anxiety. 

It  is  proper  to  state  that  what  is  called  "granite  masonry"  consists  of  a  4  feet 
ring  of  cut  granite  and  4  feet  of  dressed  granite  coping;  the  interior  to  be  made  up 
of  large  irregular  masses  of  stone,  set  in  concrete,  exactly  as  was  done  in  the  case  of 
the  piers  for  the  "Forth  Bridge." 

The  estimate  of  cost  of  the  river  pier  and  the  New  York  pier  ie  herewith  given  in 
detail,  together  with  the  cost  of  superstructure,  and  other  items  to  make  up  the  total 
cost  of  the  bridge  proper,  from  which  it  will  appear  that,  with  a  span  of  2,300  feet 
between  centers  of  towers  (or  a  clear  span  of  upward  of  2,000  feet),  the  limit  of 
what  has  been  found  to  be  a  practicable  expenditure  is  reached. 

In  view  of  the  evidence  presented,  you  are  respectfully  requested  to  consider  favor- 
ably the  following  propositions : 

(1)  That  a  2,000  feet  clear  span  is  the  longest  practicable  span  wherewith  to  cross 
the  North  River,  at  the  point  indicated. 

(2)  That  any  increase  of  span,  short  of  the  entire  width  of  the  river,  viz,  3,130  feet 
in  the  clear,  would  correspondingly  restrict  the  free  use  of  wharves  on  the  New  Jer- 
sey side. 

(3)  That  the  cost  of  a  river  pier,  at  any  point  between  the  present  location  and  say 
500  feet  from  the  New  Jersey  side,  would  be  practically  the  same  as  already  esti- 
mated ;  whereas,  the  cost  of  the  superstructure  would  increase  materially  with  the 
length  of  the  span. 

(4)  That  the  position  of  the  river  pier,  assumed  at  2,000  feet  in  the  clear  from  the 
New  York  side,  would  be  wholly  within  the  space  set  apart  as  anchorage  grounds  on 


BRIDGE  ACKOSS  THE  HUDSON  RIVEK. 


57 


the  New  Jersey  side;  as  indicated  by  diagram  attached  hereto  (taken  from  the  New 
York  Times  of  Thursday,  September  7,  1893) ;  from  which  it  will  be  seen  that  1,500 
feet  was  assumed  to  be  sufficient  for  the  free  and  unobstructed  navigation  of  the 
Hudson  at  that  point. 

And  further,  that  such  pier,  when  provided  with  suitable  warning  signals,  would 
be  a  positive  advantage  to  navigation  in  time  of  fog. 

And  further,  that  the  piers  of  the  Poughkeepsie  bridge,  crossing  the  Hudson  River 
75  miles  above,  are  500  feet  apart  in  the  clear,  and  have  not  proved  a  serious  obstruc- 
tion. 

And  further,  that  the  main  ship  channel  to  New  York  Harbor  is  1,000  feet  wide. 

(5)  That  the  superstructure  of  a  span  without  a  pier  in  the  river,  for  which  it  would 
be  necessary  to  have  a  clear  reach  between  centers  of  towers  of  3,350  feet,  would 
cost  at  least  three  times  as  much  as  the  estimate  herewith  submitted;  and  the  total 
cost  of  the  bridge  proper  would  be  more  than  double  the  estimate  for  a  2,000  feet 
span. 

We  have  no  hesitation  in  saying  that,  at  such  an  increase  of  cost,  it  would  be 
impossible  to  raise  the  necessary  capital ;  and  that,  therefore,  the  bridge  would  be 
impracticable. 

In  arriving  at  this  conclusion  we  have  been  guided  by  the  carefully  digested 
opinions  of  men  of  large  means,  who  have  expressed  a  firm  belief  in  the  enterprise, 
if  kept  within  the  j)rescribed  limit  of  cost;  and  from  whom  we  should  expect  sub- 
stantial assistance  in  perfecting  a  sound  financial  basis  of  operations. 

I  do  not  wish  to  be  understood  as  admitting  that  a  bridge  of  3,350  feet  can  be 
constructed  as  a  safe  structure. 

We  have  made  some  preliminary  estimates  of  strains  for  such  a  span,  and  the  pro- 
portions have  become  so  enormous  as  to  raise  very  grave  doubts  in  our  minds  of  the 
possibility  of  designing  such  a  structure,  with  sufficient  rigidity  to  hold  up  its  own 
weight — to  pass  the  traffic — and  to  resist  wind  pressure. 

All  of  which,  and  such  other  data  as  may  be  in  my  power  to  procure,  is  placed  at 
your  service. 

In  inclosure  No.  1  will  be  found  data  upon  which  the  estimate  of  probable  traffic 
is  based. 

In  inclosure  No.  2  references  are  given  to  loads  upon  masonry  and  foundations  as 
they  have  been  hurriedly  collected. 

The  following  plans  accompany  this  report : 

Five  copies,  pier  foundation. 

Five  copies,  plan  of  river,  with  borings. 

Ten  copies,  profile  at  proposed  crossings. 

Three  copies,  strain-sheets  of  superstructure. 

One  copy,  articjfe  from  the  New  York  Times,  September  7,  1893. 

Charles  Macdonald, 

Of  Union  Bridge  Company, 
Xo.  1  Broadway,  Neio  York. 

Maj.  C.  W.  Raymond, 

Chairman  Board  of  Engineers  appointed  by  the  President  upon  the  matter  of 
length  of  span  of  the  New  York  and  Xew  Jersey  bridge  orer  the  Hudson  River. 


NOTES  AS  TO  PRESSURES  ON  MASONRY  AND  FOUNDATIONS. 

[Collingwood,  "Masonry  East  River  Bridge,"  Transactions  Am.  Soc.  C.  E.,  Vol.  VI,  pp.  8  and  9  ] 

Weight  per  cubic  foot:  Granite  masonry,  153  pounds;  concrete,  120  pounds. 
Pressure  on  central  shaft,  26  tons  per  square  foot. 

[Cresy,  "Encyclopedia  of  Engineering,  1847.'  ] 

(Page  705.)  Five  and  one-half  tons  on  9  square  inches,  1,370  pounds  per  square 
inch,  has  stood  for  several  centuries.  "Chapter  House  at  Elgin."  Two  columns  in 
the  Church  Toussant  d'Augers,  12  inches  diameter  and  height  25  feet,  carrying  pointed 
arches;  load  on  each,  25  tons,  or  400  pounds  per  square  inch. 

(Page  706.)  Piers:  Dome  St.  Peters,  1,022^  pounds  on  9  square  inches,  or  113 
pounds  per  square  inch;  St.  Paul's,  1,190  pounds  on  9  square  inches,  or  132  pounds 
per  square  inch;  Invaliues,  992  pounds  on  9  square  inches,  or  102  pounds  per  square 
inch;  St.  Geuevieve,  1,840  pounds  on  9  square  inches,  or  201  pounds  per  square  inch. 
Columns:  St.  Paul's,  without  the  walls,  1,235  pounds  on  9  square  inches,  or  137 
pounds  per  square  inch;  Church  Toussant  d'Augers,  2,767  pounds  on  9  square  inches, 
or  307  pounds  per  square  inch. 

The  above  is  quoted  from  "Rondelet,  Traite  d'Arckitecture." 


58 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


[John  Newman,  <(  Cylinder  Bridge  Piers,"  approximate  safe  loads  per  square  foot.] 

Firm  sand  in  estuaries  and  bays,  5  to  5.6  tons.  Dutch  engineers  consider  safe 
loads  on  firm,  clean  sand  6  to  6.16  tons.  Very  firm,  compact  sand — foundations  at 
considerable  depth,  not  less  than  20  feet — and  sandy  gravel,  6.7  to  7.84  tons.  Firm 
shale  and  clean  gravel,  6.7  to  8.96  tons.    Compact  gravel,  7.84  to  10.08  tons. 

Clean  sand,  homogeneous  Thames  gravel,  has  been  weighted  with  280  cwt.  per 
square  foot  at  3  to  5  feet  below  the  surface,  and  showed  no  signs  of  failure,  15.68 
tons. 

[Gaudard,  "Foundations."] 

Stiff  clay,  marl,  sand,  or  gravel,  55  to  110  cwt.  (3.08  to  6.16  tons).  Gorai  bridge 
(close  sand),  Lock  Kew  (gravel),  Bordeaux  (gravel),  165  to  183  cwt.  Nantes  (sand), 
152  cwt.,  some  settlement.  Szegedin  (clay  and  fine  sand),  133  cwt.  (7.4  tons),  rein- 
forced by  driving  piles  in  interior  of  cylinder,  and  sheathing  outside.  Charing 
Cross,  cwt.,  159,  including  adhesion  (8.9  tons).  Cannon  street,  117  cwt.,  including 
adhesion  (6.5  tons).    Roque  Favor  aqueduct,  258  cwt.,  rocky  ground  (14.4  tons). 

[Leslie,  "  Transactions  Institute  of  Civil  Engineers,  January  24,  1888."] 

Hooghly  Jubilee  bridge,  10  tons  net. 

[Engineering  News,  March  14,  1885.] 

Washington  monument :  Area  of  base,  126.5  feet  by  126.5  feet,  16,000  square  feet. 
Weight,  81,120  (long  tons),  90,850  (short  tons).  Average  pressure  on  base  (exclusive 
of  wind),  11,340  pounds,  or  5.67  tons  per  square  foot.  Taking  out  area  45  feet  square, 
2,025  feet,  leaves  balance  under  concrete,  14,000  square  feet  (nearly).  Average  per 
square  foot  under  concrete,  90,850  —  14,000,  6.5  tons. 

Square  feet. 


Area  of  bottom  of  buttress,  101.5  square   10,  302 

Less  45  square   2,  025 


Effective  area   8,  277 

Tons. 

14,000  by  13  feet,  182,000  by  150    13,  650 


Original  weight   90,  850 

Less   13,650 


77,  200 

On  line  c  —  c,  pressure  77,200  -r  8,277,  9.32  tons  per  square  foot. 
Area  at  c  —  c,  55  square,  3,025  —  25  square,  2,400  square  feet. 

Weight  of  buttress,  101.5  square  10,  302 

55  square   3,025 

4  by  78  square        24,  336 


37,  663  -  6,  6,277  by  150  by  25  =  23,540,000 
pounds,  11,770  tons. 
Weight  of  shaft,  77,200  —  11,770,  65,430  tons. 

Average  per  square  foot,  65,430  -f-  2,400  square  feet,  27.2  tons  per  square  foot. 
Material  is  marble. 

At  bottom  of  foundations,  5.67  tons  per  square  foot;  at  bottom  of  buttress,  9.32 
tons  per  square  foot;  at  bottom  of  shaft,  27.2  tons  per  square  foot;  all  exclusive  of 
wind. 

Bunker  Hill  Monument :  On  hard  sand  and  gravel,  54  tons,  no  settlement. 

Tower  of  brick  church  (Thirty-seventh  street  and  Fifth  avenue) :  On  hardpan, 
7  tons  per  square  foot,  some  settlement. 

Crushing  strength  of  concrete,  department  of  docks :  1:2:5(1  foot  cube).  Hard- 
ened in  water  forty-five  days,  425  pounds  square  inch,  30.5  tons  square  foot.  Hard- 
ened in  water  one  year,  1,520  pounds  square  inch.  Hardened  in  air  one  year,  1,620 
pounds  square  inch. 

REVENUE  STATISTICS. 

I  regret  to  say  that  much  of  the  detailed  information  which  I  expected  to  submit 
in  this  appendix  has  been  forwarded  to  London,  but  the  following  will  be  of  interest  : 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


59 


Xorth  River  ferries,  passengers  carried  yearly. 


Staten  Island   5,  445,  800 

Jersey  Central   10,  938,  320 

Pennsylvania   14.  589,  050 

Barclay   12,899,100 

Chambers   10,  868,  240 

Jay   2, 164,  640 

Desbrosses   8,067,960 

Christopher   11,  739, 130 

Fourteenth  street   2,  811,  960 

Twenty-third  street   3,  594,  520 

Forty-second  street   1,  744,  680 


Total   84,663,400 


The  number  of  people  crossing  the  East  River  ferries  is  slightly  in  excess  of  the 
above,  or  more  exactly  88,663,500;  but  this  is  exclusive  of  the  people  who  cross  the 
Brooklyn  bridge. 

These  latter  amounted  to  42,615,105  in  1893. 

From  the  opening  of  the  railway  to  public  use,  September  24,  1883,  to  November 
30,  1893,  inclusive,  a  period  of  ten  years  and  sixty-seven  days,  304,875,286  passengers 
were  carried.  During  any  month  the  greatest  number  transported  was  4,033,920 
in  October,  1892,  which  included  the  week  from  the  8th  to  the  15th  of  the  Colum- 
bian festival.  The  next  greatest  number  was  3,846,493,  in  May,  1893,  an  average  of 
124,080  per  day.  In  one  day  of  twenty-four  hours,  the  maximum  number  carried  was 
223,625,  on  October  12,  1892,  during  the  Columbian  festival;  the  next  greatest  num- 
ber was  166,403,  on  Januarv,  14;  and  the  minimum  number  during  the  official  year 
1893  was  45,280,  on  August  20. 

In  1884,  the  year  after  the  opening,  the  total  number  of  passengers  passed  over  the 
bridge  was  8,828,200. 

The  average  number  of  cars  of  freight,  inbound  and  outbound  daily,  on  the  fol- 
lowing-named railroads,  via  New  York  and  Jersey  City,  during  the  year  1890,  as  far 
as  statistics  have  been  obtained,  is  as  follows: 


9 

Pennsyl- 
vania 
Eailroacl. 

Erie. 

West 
Shore. 

Delaware. 

Lacka- 
wanna and 
Western. 

Jersey 
Central. 

Various. 

318 
724 
300 

322 
694 
210 

130 
260 

144 

402 
210 

138 
328 
200 

48 

244 

1,342 

1,  226 

390 

756 

666 

292 

Grand  total,  4,672  cars  daily;  1,705,280  cars  during  year. 


Among  the  above  items  of  freight  which  could  be  handled  to  advantage  in  New 
York  may  be  mentioned — 

Milk  daily  carloads . .  53 

Flour  and  meal  . .  do   397 

Produce  do   407 

Grand  Central  Station.— Total  passengers  per  day,  35,000;  or  12,250,000  per  year. 


St.  Louis  bridge. 


1890. 

1891. 

1892. 

1893. 

Passenger  coaches  

259, 187 
178, 197 
111,  350 
46, 775 
12.  948 
$4.  50 
1,940 
1,  367, 184 
25.84 
4,  149 
41.77 

224,  784 
132, 187 
115, 942 
50,  009 
609 
$4.34 
1,434 
1,  375,  057 
26. 15 
4,231 
46.  57 

232, 259 
141,062 
125,  676 
50, 696 
4,847 
$4.  46* 
1.515" 
1,  522,  037 
21.7 
4,  642 
44.94 

214.816 
139.  023 
128, 601 
51,568 
7,  605 
$4.58 
1,484 
1,  587,  549 
24.6 
4,  848 
43.31 

Revenue  per  loaded  car.  

Average  number  of  cars  per  dav  

Keveuue  per  passenger   cents. . 

60  BRIDGE  ACROSS  THE  HUDSON  RIVER. 


It  has  been  assumed  that  the  suburban  traffic  which  can  be  brought  into  the 
terminal  of  the  North  River  bridge,  at  Forty-second  street  and  Seventh  avenue, 
will  equal,  if  it  does  not  exceed,  that  which  is  delivered  at  the  Grand  Central  Station, 
Forty-second  street  and  Fourth  avenue ;  and  that  of  the  western  passenger  traffic 
now  reaching  New  York,  of  which  70  per  cent  is  carried  by  the  New  York  Central 
system,  against  30  per  cent  by  all  other  lines,  a  very  considerable  diversion  will 
take  place  in  favor  of  the  new  terminal. 

Based  upon  this,  the  total  number  of  passengers  paying  toll  over  the  bridge  has 
been  taken  at  14,000,000  per  year.  Of  quick  freight,  including  express,  it  is  safe  to 
count  upon  1,000  cars  per  day ;  or,  say,  350,000  per  year. 

In  assuming  a  rate  which  it  would  be  safe  to  charge,  per  passenger  and  per  car, 
the  cost  of  motive  power  has  been  eliminated;  that  is  to  say,  the  cost  of  moving 
the  passengers  and  cars  would  be  borne  by  the  railroads  transporting  them. 

Under  this  assumption,  an  average  of  15  cents  per  passenger  and  $4  per  car  gives 
a  gross  income  as  follows : 


14,000,000  passengers,  at  15  cents   $2, 100,  000 

350,000  cars,  at  $4   1,  400, 000 


Gross  income   3,  500, 000 

Less  repairs,  taxes,  and  sundries  (about  36  per  cent)   1,  250,  000 


Net  income   2,250,000 

By  reference  to  the  St.  Louis  bridge  charges  for  freight  and  passengers,  which 
include  cost  of  motive  power,  these  rates  are  moderate. 

Estimated  cost  of  New  York  and  New  Jersey  bridge. 

Superstructure,  230,000,000  pounds,  at  44  cents   $10,  350.  000 

River  pier   3,500,000 

New  York  pier   2,  300,  000 

New  Jersey  anchorage   400, 000 

New  York  anchorage   100,  000 

Tracks,  4,000  linear  feet,  at  $2.50  X  6    60,  000 

Interest   2,  000,  000 

Contingencies   1,  890,  000 


20,  000,  000 

Add  10  per  cent   2,  000,  000 


Total   22,000,000 

Estimated  cost  of  river  pier,  on  basis  of  60  feet  diameter  on  top  and  100  feet  diameter 
on  bottom,  ivith  inclined  sides. 

Excavation,  1,178.100  cubic  feet,  at  27i  cents   $324,  000 

Concrete,  38,733  cubic  yards,  at  $6    232,  400 

Steel,  3,000,000  pounds,  at  3  cents   90,  000 

Masonry,  8,600  cubic  yards,  at  $15    129,  000 


Cost  of  one  cylinder   775,  400 


Cost  of  pier,  $775,400  x  4  cylinders   3, 101,  600 

Add  10  per  cent   310,  000 


3,  411,  000 

Test  pier   89.  000 


Total  cost  of  river  pier,  say   3,  500,  000 


BRIDGE  ACROSS  THE  HUDSON  RIVER.  61 

Detailed  weight  of  New  York  and  New  Jersey  bridge. 

Suspended  span,  720  feet  c  to  c  end  pins :  Pounds- 
Top  chords   2,  400,  000 

End  posts   1,900,000 

Bottom  chords   2,  900,  000 

Web  eyebars   1,500,000 

Vertical  posts  and  braces   800,  000 

Pins   200,  000 

Lateral  system   700,  000 

Stringers   2,  500,  000 

Cross  floor  beams   1,  600,  000 


14,  500,  000 


Two  cantilever  arms : 

Top  chord  eyebars   13,  400.  000 

Web  eyebars   7,  500,  000 

Bottom  chords   15,  800.  000 

Pins   1,000,000 

Web  compression  members   9,  000,  000 

Lateral  system   2,  800,  000 

Stringers   5,  000,  000 

Cross  floor  beams   4,  200,  000 

Sundries   3,300,000 


62, 000,  000 


Two  anchorage  arms,  840  feet  c  to  c  end  pins: 

Eyebars   21,  200,  000 

Bottom  chords     21,  000,  000 

Web  compression  members   34,000,000 

Pins   2.  000,  000 

Lateral  system   3,  500,  000 

Stringers   5,  500,  000 

Cross  floor  beams   5,  000,  000 

Sundries   3,300,000 


9  95,  500,  000 


Two  center  towers : 

Eyebars   6,  900,  000 

Tower  vertical  posts   24,  900,  000 

Bottom  chords   5,900.000 

Lateral  system   11,  600,  000 

Stringers   1, 100,  000 

Cross  floor  beams   1,900,000 

Bedplates   5,  700,  000 


58,  000,  000 


Totals : 

Suspended  span   14,  500.  000 

Two  cantilever  arms   62,  000,  000 

Two  anchorage  arms   95,  500,  000 

Two  to wers   58,  000,  000 


230,  000,  000 


Appendix  C. 

STATEMENT  OF  MR.  GUSTAV  H.  SCHWAB,  CHAIRMAN  SPECIAL  COMMITTEE,  CHAMBER 
OF  COMMERCE  OF  THE  STATE  OF  NEW  YORK,  ON  HUDSON  RIVER  BRIDGE. 

New  York,  July  17,  1894. 
Gentlemen  :  In  accordance  with  your  permission  I  avail  myself  of  your  courtesy 
to  present  to  you  the  views  of  the  Chamber  of  Commerce  of  the  State  of  New  York 
as  represented  by  its  special  committee  on  the  Hudson  River  bridge. 


62 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  Chamber  of  Commerce  ou  December  7  last  adopted  the  following  resolutions: 

"Resolved,  That  in  the  opinion  of  this  Chamber  the  passage  by  Congress  of  any 
Bill  permitting  the  construction  of  a  bridge  across  the  Hudson,  with  piers  in  the 
river  bed,  will  be  an  obstruction  to  the  commerce  of  this  Port  and  an  injury  to  the 
entire  country,  particularly  to  the  great  West,  whose  products  find  an  outlet  through 
the  Erie  Canal  and  the  Hudson  River. 

"Resolved,  That  the  Representatives  in  Congress  from  this  State  be  requested  to 
strenuously  oppose  the  passage  of  any  Act  which  will  permit  the  building  of  piers 
or  other  obstructions  in  the  river  bed." 

The  objections  urged  by  the  chief  commercial  body  of  this  city  against  the  proposed 
location  of  a  pier  or  piers  in  the  Hudson  River  between  the  pier-head  lines,  opposite 
the  city  of  New  York,  are  the  following: 

The  lower  part  of  the  Hudson  River  not  only  serves  the  purposes  of  river  traffic 
and  of  the  accommodation  of  the  enormous  trade  that  finds  its  way  from  the  great 
West  through  the  Erie  Canal  to  tidewater,  and  from  the  brick,  lumber,  and  stone 
yards,  manufactories  and  icehouses  along  the  river,  but  this  great  river  between 
the  New  York  side  and  the  New  Jersey  shore  furnishes  such  a  harbor  as  can  not  be 
found  in  any  other  part  of  the  world.  It  provides  the  most  varied  kind  of  traffic — by 
steamers,  ferryboats,  schooners,  lighters,  rafts,  barges,  large  sailing  vessels,  and. 
yachts — with  accommodation,  and  renders  it  possible  for  the  largest  ocean  steam- 
ers to  safely  maneuver  throughout  its  whole  extent.  Although  at  the  present  time 
the  piers  accommodating  ocean-steamship  traffic  do  not  extend  much  above  the  pro- 
posed site  of  the  New  York  and  New  Jersey  bridge,  it  can  not  be  doubted  that  with 
the  rapid  growth  of  commerce  and  navigation  of  this  port,  the  whole  shore  line 
within  the  city  limits  of  New  York  on  the  Hudson  River  will  be  ultimately  taken  up 
in  pier  accommodations,  as  well  as  the  opposite  shore  on  the  New  Jersey  side.  This 
appears  a  safe  prediction,  in  view  of  the  fact  that  thirty  years  ago  the  harbor  ship- 
ping of  New  York  did  not  extend  beyond  Tenth  street.  At  present  it  has  reached 
Seventieth  street,  and  on  the  New  Jersey  side  there  are  now  plans  in  contemplation 
and  partly  in  execution  for  the  building  of  piers  as  high  as  Eighty-sixth  street. 

In  connection  with  this  extension  of  harbor  traffic  it  should  be  borne  in  mind  that 
ocean  steamshipstendtogrow  larger,  and  that  the  space  required  for  their  maneuver- 
ing should  therefore  also  be  larger.  It  is  for  this  reason  that  the  East  Riveris  not  used 
for  the  handling  of  large  transatlantic  steamers,  but  that  these  steamers  find  their 
docks  on  the  North  River,  which  is  by  far  the  most  important  part  of  the  gre  at  harbor  of 
New  York,  the  importance  of  which  is  shown  by  the  fact  that  by  a  recent  bill  inCon- 
gress  the  port  of  New  York  will  now  include  Yonkers.  The  placing  of  ajpier  or  piers 
in  the  river  bed  at  any  point  between  the  pierhead  lines  will,  inevitably,  seriously 
interfere  with  the  maneuvering  of  these  ocean  steamers,  as  well  as  with  harbor 
traffic  in  general.  The  obstruction  to  harbor  navigation  and  the  great  danger  to 
life  involved  in  the  construction  of  a  pier  or  piers  in  the  river  bed  must  be  patent  to 
anyone  who  has  crossed  the  Hudson  River  in  foggy,  thick,  or  stormy  weather.  It 
is  to  be  feared  that  the  placing  of  a  pier  almost  in  the  center  of  the  river  will 
result  not  only  in  an  obstruction  to  the  passage  of  ice  in  the  winter  months,  but  will 
cause  the  formation  of  shoals  around  the  abutments  of  such  piers. 

The  current  in  the  Hudson  River  opposite  the  city  of  New  York  does  not  pursue  a 
course  parallel  with  the  river  banks,  but  runs  diagonally  across  from  shore  to  shore, 
thereby  causing  thegreatest  difficulty  in  handling  tows  and  floats  in  the  harbor.  The 
location  of  a  pier  in  the  river  would  greatly  increase  the  difficulties  aud  dangers  of 
harbor  navigation  to  those  tows,  and  should  a  tow  of  canal  boats  or  a  steamer  laden 
with  passengers  on  this  crowded  waterway  have  the  misfortune  to  come  into  contact 
with  the  abutments  of  these  bridge  piers,  the  serious  consequences  to  life  and  prop- 
erty can  well  be  imagined. 

The  argument  has  been  made  in  favor  of  the  bill  that  the  proposed  pier  is  to  be 
placed  in  the  anchorage  grounds,  and  not  in  the  main  channel.  If  this  is  so,  the 
argument  displays  l^ck  of  information,  for  a  pier  placed  in  the  anchorage  grounds 
would  render  a  large  part  of  such  grounds  useless.  No  vessel  of  any  size  could  with 
safety  anchor  within  a  circle  of  2,400  feet  in  diameter  of  which  the  bridge  pier  would 
be  the  center. 

We  believe  that  the  existence  of  a  natural  rocky  island,  or  islands,  of  the  extent 
of  the  proposed  bridge  pier,  in  the  same  location  in  the  river  would  never  be  toler- 
ated, and  that  millions  of  dollars  would  have  been  spent  long  ago  to  remove  such 
serious  obstructions  to  navigation  in  the  river  and  harbor,  aud  in  view  of  the  expend- 
itures of  the  Government  for  the  purpose  of  removing  natural  obstructions,  the 
deliberate  erection  of  artificial  barriers  would  appear  to  be  the  greatest  folly 

The  reasons  against  the  pier  were  so  convincing  upon  the  legislature  of  the  State 
of  New  York  that  the  act  giving  a  charter  to  the  New  York  and  New  Jersey  Bridge 
Company  insisted  upon  a  singlAspan  for  this  bridge.  The  company  then  appealed 
to  Congress  for  permission  to  plafi*  a  pier  in  the  river ;  the  President,  however,  vetoed 
the  bill,  in  view  of  the  danger  to  the  commercial  and  navigation  interests  of  the  first 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


63 


port  of  this  country.  As  the  bridge  company  represented  in  Congress  that  a  span  of 
over  2,000  feet  was  a  practical  impossibility,  your  honorable  Board  was  appointed  by 
the  President  to  examine  into  the  question  thoroughly,  whether  a  bridge  could  bo 
built  longer  than  2,000  feet  span,  which,  in  this  case,  means  a  span  over  the  entire 
river,  for  if  built  for  2,100  or  2,300  feet  it  would  still  leave  a  dangerous  obstruction 
in  the  river  between  the  pierhead  lines,  and  would  make  thoNew  Jersey  shore  intho 
vicinity  practically  useless  for  dock  purposes.  This,  then,  is  the  question  that  comes 
before  your  honorable  Board,  namely,  whether  a  bridge  can  be  built  over  tlie  river 
with  a  single  span  which  would  be  practicable  and  not  prohibitive  in  cost. 

There  is  no  rule  by  which  the  practicability  as  to  cost  can  bo  determined,  but  in 
the  view  that  a  bridge  with  no  pier  in  the  river  can  bo  built  at  a  cost  that  is  not 
prohibitive  the  commercial  and  navigation  interests  of  this  port  find  themselves 
supported  by  Mr.  Thomas  C.  Clarke,  the  chief  engineer  of  the  New  York  and  New 
Jersey  Bridge  Company  in  his  report  to  the  company  of  March  15, 1892,  submitted. to 
the  U.  S.  Senate  on  March  23, 1892.  In  this  report  Mr.  Thomas  C.  Clarke,  the  chief 
engineer  of  the  New  York  and  New  Jersey  Bridge  Company,  states  as  follows: 

"  I  expect  to  be  able  to  have  plans  and  estimates  of  cost  of  the  suspension-canti- 
lever bridge,  requiring  no  pier  in  the  river  between  the  pierhead  lines,  ready  by 
April  1st.    *    *  * 

''I  am  now  prepared  to  say  that  if  they  decide  that  thero  shall  be  no  pier  in  the 
river,  I  can  build  you  a  bridge  on  the  combined  suspension-cantilever  plan  that  sliall 
be  strong  enough  and  stiff  enough  to  carry  trains  at  20  miles  an  hour,  and  at  a  cost 
that  shall  not  be  prohibitory." 

These  views  of  Mr.  Thomas  C.  Clarke,  chief  engineer  of  the  Noav  York  and  New 
Jersey  Bridge  Company,  have  the  indorsement  of  Mr.  W.  A.  Roebling,  who  has  writ- 
ten to  me  under  date  of  June  21  last  as  follows: 

"I  am  not  familiar  with  the  proposed  designs  for  this  work,  but  may  say  in  gen- 
eral that  a  cantilever  with  two  spans  of  2,000  feet  each  is  considered  feasible,  and 
that  a  suspension  bridge  with  a  single  span  of  3,000  feet  is  also  feasible,  with  some 
increase  in  cost.  Such  a  span  is  within  the  carrying  capacity  of  a  commercial  qual- 
ity of  steel  wire."    *    *  * 

Mr.  Roebling  also  states  as  follows:  "I  will  close  by  saying  that  only  two  years 
ago  the  promoters  of  the  New  York  &  New  Jersey  Bridge  Co.  had  determined  to 
adhere  to  the  suspension  principle,  in  which  I  was  consulted,"  "  *  *  thus 
amply  corroborating  the  statements  of  the  chief  engineer  of  the  New  York  and  New 
Jersey  Bridge  Company. 

The  Chamber  of  Commerce  of  the  State  of  New  York  has  retained  Mr.  William 
Hildenbraud,  recommended  to  them  by  Mr.  W.  A.  Roebling,  and  one  of  his  most 
trustworthy  assistants  for  many  years,  for  the  purpose. of  presenting  to  you  tech- 
nical arguments  in  favor  of  a  single  span  over  the  whole  river,  with  its  probable 
cost,  its  practicability,  and  safety. 

GUSTAV  H.  SCHWAB, 

Chairman  Special  Committee  on  Hudson  Hirer  bridge, 

Chamber  of  Commerce  of  the  State  of  New  York. 
The  Board  of  Engineers  on  Hudson  River  Bridge  Span. 


Appendix  C1. 

LETTER  OF  MR.  W.  HILDENBRAND  TO  MR.  GUSTAV  II.  SCHWAB. 

New  York,  July  12,  1S94. 

Dear  Sir:  In  answer  to  your  question  whether  it  be  possible  to  construct  a  prac- 
tical railroad  bridge  across  the  Hudson  River  at  or  near  Sixty-ninth  street  without 
a  pier  between  pierhead  lines,  I  do  not  hesitate  to  say  yes,  and  beg  to  submit  to  you 
the  following  data,  which  will  demonstrate  by  figures  that  a  suspension  bridge  of 
over  3,000-foot  span  is  not  only  an  engineering  possibility,  but  also  will  compare, 
from  a  commercial  point  of  view,  not  unfavorably  with  a  cantilever  bridge  of  2,100- 
foot  span,  as  suggested  by  the  New  York  and  New  Jersey  Bridge  Company. 

The  design,  as  submitted  to  you,  must  be  considered  as  a  mere  preliminary  sug- 
gestion which  might  undergo  many  changes  if  the  problem  bo  worked  out  in  detail, 
but  the  calculations  6how  what  can  be  done,  and  I  am  confideut  to  say  that  the 
weight  of  the  metal  and  the  cost  as  given  will  not  be  far  from  correct  figures  of 
carefully  prepared  plans  and  estimates. 

From  a  profile  of  the  river,  shown  in  a  sketch  of  the  proposed  cantilever  bridge, 
published  in  the  Scienti  lie  American  of  June  10,  it  appears  that  the  distance  between 
pierhead  lines  is  about  3,000  feet,  consequently  the  length  of  a  single-span  bridge 
S.  Ex.  1  10 


64 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


was  assumed  to  be  3,200  feet  from  center  to  center  of  towers,  allowing  200  feet  for 
the  width  of  the  latter. 

Most  engineers  will  agree  that  the  suspension  principle  is  the  only  practical  solu- 
tion for  a  bridge  of  that  length;  hence,  without  trying  any  other  kind  of  construc- 
tion, all  calculations  are  based  on  a  design  for  a  suspension  bridge  consisting  of  wire 
cables  and  stiffened  by  a  truss  with  three  hinges.  This  is  not  the  most  economical 
construction,  but  it  was  chosen  for  the  purpose  of  showing  the  practicability  and 
economy  of  such  a  design,  even  under  unfavorable  conditions,  and,  on  account  of  all 
forces  and  strains  being  statically  determinate,  of  easy  comparison  with  a  cantilever 
or  other  structure. 

A  suspension  bridge  is  never  entirely  rigid,  because  the  contraction  and  expansion 
of  the  cables  under  changes  of  temperature  cause  the  floor  to  drop  or  rise  to  the 
extent  of  several  feet.  An  absolute  stiffening  of  the  floor  against  distortion  under 
one-sided  loads  would,  therefore,  be  a  waste  of  material,  hence  the  stiffening  girder 
for  this  assumed  design  was  constructed  only  with  such  rigidity  that  the  simulta- 
neous depression  and  rise  of  the  floor  under  a  one-sided  load'would  create  no  steeper 
grade  than  1|  per  cent,  or  about  the  same. as  is  caused. by  the  rise  and  fall  in  conse- 
quence of  extreme  temperatures.  Keeping  these  conditions  in  view,  the  following 
are  the  principal  features  and  dimensions  of  this  bridge: 


Total  length  from  face  to  face  of  anchorage  feet. ..  4, 900 

Main  span  from  center  to  center  of  towers  do  3,  200 

Width  of  tower  at  water 'line  do   200 

Width  of  tower  at  floor  line,  about  do  *  100 


Eastern  end  span  will  consist  of  two  independent  truss  bridges,  each  of  400-foot  span. 
Western  end  span  will  consist  of  three  independent  truss  bridges,  each  of  266-foot 
sjjan. 


Deflections  of  cable: 

Main  span  at  55°  F  feet ...  322 

Main  span  at  0°  do   319. 18 

Main  span  at  110°  do   324.  77 

Rise  and  fall  of  cable  and  floor  for  a  variation  of  110°  do   5. 59 

Length  of  cable  in  main  span  at  55°  F  do   3,  285. 26 

Length  of  cable  from  anchorage  to  anchorage  do   5, 120 

Deflection  of  back  cable  from  a  straight  line  connecting  top  of  tower  and 
face  of  anchorage : 

For  dead  load  feet ...  9.8 

For  dead  and  live  load  do   7.2 

Depression  of  center  span  when  fully  loaded : 

Arising  from  the  elongation  of  cable  of  5,120  feet  length  do   4. 21 

Arising  from  the  change  of  deflection  in  back  cable  do   .5 

Total  rise  and  fall  of  floor  in  center  of  bridge  under  extremes  of  tempera- 
ture and  load  feet. . .  10.  3 

Camber  of  floor  at  55°  F  ,  do   8 

Grade  of  floor  at  55°  F  per  cent. .  1 

Grade  of  floor  at  0°  F  do ... .  1. 35 

Grade  of  floor  at  1 10°  F  do ... .  .66 

Camber  of  floor  at  110°  and  floor  fully  loaded  feet. . .  .62 


From  these  figures  it  appears  that  the  maximum  grade  of  the  floor  is  less  than 
1^  per  cent,  and  that  the  floor,  when  fully  loaded  in  the  warmest  weather,  will 
never  sink  below  level. 

The  height  of  the  towers  will  be  determined  by  the  following  figures : 

Feet 


From  high  water  to  under  side  of  bridge   150 

Thickness  of  floor   8 

Camber  of  floor   8 

Bottom  of  cable  above  floor  in  center   2 

Deflection  of  cable   322 

Extra  height  of  tower  to  support  two  or  three  tiers  of  cables   20 

Total  510 


The  bridge  is  supposed  to  carry  six  railroad  tracks,  and  the  live  load  is  assumed  to 
be  18,000  pounds  per  linear  foot,  covering  the  whole  span  from  tower  to  tower. 

If  the  moving  load  were  but  4,500  pounds  per  linear  foot,  and  one-half  the  span 
be  covered  with  the  same,  it  can  be  shown  that,  without  any  sti Honing  construc- 
tion, the  floor  would  doliect  6.01  feet  at  one  quarter  of  the  span  and  rise  5.23  feet  at 
the  opposite  quarter,  making  a  total  difference  of  11.24  feet  in  1,600  feet,  or  a  grade 
of  1.4  per  cent.    This  is  admissible;  hence  the  stiffening  girder  must  be  calculated 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


G5 


to  resist  a  live  load  of  13,500  pounds  per  linear  foot,  and  must  be  dimensioned  to 
deflect  not  over  6  feet  in  the  quarter  span.  The  span  of  the  stiffening  girder  is 
3,100  feet,  and  its  height  was  assumed  80  feet,  or  one-fortieth  of  the  span. 

According  to  the  theory  of  stiffening  girders,  as  shown  by  Rankine,  the  loaded 
half  of  the  truss  must  be  calculated  for  a  uniformly  distributed  load  of  pounds 
per  foot,  and  the  unloaded  half  for  the  same  force,  acting  upward,  deflecting  the 
girder  thus : 


Assuming  a  unit  strain  of  20,000  pounds  per  square  inch  the  max.  chord  section  is 
1,266  square  inches  (=  633  square  inches  for  one  chord  of  each  of  two  trusses); 
the  average  weight  of  chords,  7,332  pounds  per  foot  (=  1,833  pounds  for  one  chord  of 
each  of  two  trusses) ;  the  average  weight  of  web  members,  3,048  pounds  per  foot; 
total,  10,380  pounds  per  linear  foot. 

Calculating  the  deflection  of  this  truss,  it  wiil  be  found  to  be  4.58  feet,  if  the 
elongation  and  contraetion  of  the  web  members  and  the  separate  moment  of  inertia 
of  each  chord  be  neglected.    The  true  deflection  would  therefore  not  exceed  6  feet. 

The  weight  of  the  platform  per  double  track  is  about  the  same  as  that  of  any 
first-class  railroad  bridge,  viz,  1,800  pounds  per  linear  foot. 

The  floor  beams  will  not  reach  across  the  six  tracks  in  one  span,  but  will  be  sup- 
ported at  two  intermediate  points;  hence  the  total  weight  of  the  platform  will  be 
5,400  pounds  per  linear  foot. 

The  aggregate  load  to  be  sustained  by  the  cables  will  be  composed  of  the  follow- 
ing weights : 

Pounds  per 
linear  foot. 

Moving  load   18,  000 

Weight  of  stiffening  truss   10,  380 

Weight  of  platform,  3,900  pounds  steel  and  1,500  wood   5, 400 

Weight  of  projecting  ends  of  floor  beam   300 

Weight  of  sway-bracing  and  intermediate  floor-beam  suspenders   810 

Weight  of  wind  cables  and  wind  bracing   1,  240 

Weight  of  suspenders   1, 110 

Weight  of  cables   12,  500 

9   

Total   49,740 

Total  load  on  cable:  12,500  X  3,200  +  37,240  X  3,100  =  77,722  tons;  tension  in 
cables  at  one-tenth  deflections  104,613  tons;  allowing  a  strain  of  30  tons  per 
square  inch,  it  requires  3,487  square  inches  or  74,570  No.  3  wires  (diameter,  0.244 
inch)  which  will  weigh  12,000  pounds  per  foot. 

Assuming  12  cables,  1  cable  will  consist  of  6,220  wires  and  will  have  a  diameter, 
including  wrapping,  of  23  inches.  With  14  cables  the  diameter  of  each  would  be  2l| 
inches. 

The  size  and  number  of  cables  may  be  varied  according  to  individual  opinion,  but 
the  above  size  may  be  advisable  for  coinciding  nearest  with  the  cables  of  the  New 
York  and  Brooklyn  bridge.  The  latter  were  designed  to  contain  6,308  wires,  but 
eventually  were  built  of  5,400  wires  of  a  heavier  size. 

There  is  no  reason  to  assume  that  larger  cables  could  not  be  made,  but  there  can 
certainly  be  no  doubt  about  the  successful  construction  of  cables  if  a  size  be  adopted 
which  is  near  the  limit  of  the  precedent  given  by  the  cables  of  the  Brooklyn  bridge. 

The  following  sketches  will  illustrate  the  general  design  : 

(  able  making  will  require  from  16  to  18  months,  including  the  accessory  work  of 
erecting  "cradle"  ropes  and  foot  bridge. 

The  time  consumed  for  making  two  of  the  Brooklyn  bridge  cables  was  9  months, 
bnt  several  methods  applied  there  could  be  improved  upon  for  shortening  the  time. 
For  instance,  all  cable  wire  was  stored  on  one  shore  and  taken  across  the  river  from 
one  side.  It  required  from  7  to  8  minutes  for  the  wire  to  travel  across,  while  regu- 
lating the  same  took  only  2  to  2\  minutes;  therefore,  the  time  for  strand  making 
can  be  shortened  one-half  if  the  wire  wheel,  instead  of  returning  empty,  would 
take  a  wire  across  from  the  opposite  shore.  To  "let  off"  and  regulate  one  strand 
required  from  3  to  4  days'  labor,  and  while  this  work  went  on  strand  making  of  the 
Brooklyn  bridge  cables  was  interrupted.  There  is  no  particular  reason  for  this,  and 
it  is  fully  practical  to  make  a  new  strand  while  another  is  regulated.  In  this  way 
the  time  of  making  cables  is  actually  confined  to  the  time  of  regulating  strands 

S.  Ex.  12  5 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


Each  of  tho  12  cables  will  consist  oithor  of  19  or  37  strands,  the  former  having 
the  advantage  of  quicker  work,  but  dealing  with  great  weights.  Tho  latter  makes 
it  easier  to  handle  tho  strands,  though  it  may  take  a  little  longer  in  regulat  ing 
them.  Assuming  37  strands,  and  3  days  for  regulating  each  strand,  tho  time  of  mak- 
ing one  cable  without  wrapping  would  be  111  days. 

Two  wrapping  machines,  working  from  the  towers  towards  tho  center,  will  wrap 
about  20  feet  per  day,  requiring  160  days  for  the  whole  span;  but  with  a  sufficient 
number  of  ''squeezers"  it  would  bo  just  as  practical  to  employ  4  or  more  wrapping 
machines  and  shorten  tho  time  accordingly.  If  the  time  for  wrapping  the  cable 
bo  reduced  to  80  days,  tho  total  time  necessary  for  making  1  cable  will  be  li»L  work- 
ing or  221  calendar  days,  which  is  less  than  7^  months.  Hence  the  above-stated 
time  of  16  or  18  months  for  tho  whole  operation  of  cable-making  gives  a  liberal 
allowance  for  contingencies  and  for  tho  erection  of  the  auxiliary  structures.  Of 
course  it  will  be  necessary  to  make  arrangements  for  constructing  all  cables  simul- 
taneously, which  can  easily  be  done,  provided  the  cables  are  not  less  than  3  or  4  feet 
apart. 

For  attaching  the  suspendors  and  making  connections  between  tho  cables,  cable 
bands  may  be  employed  which  are  made  in  two  parts,  provided  with  heavy  flanges, 
and  screwed  up  with  three  or  more  bolts  in  each  flange.  Tho  cable  bands  of  tho 
Brooklyn  bridge  wero  forged  of  one  piece  and  screwed  up  with  but  one  bolt;  they 
were  perfectly  tight  when  of  correct  size,  but  they  had  a  tendency  to  slide  when  a 
little  too  large.  Bands  made  in  two  parts,  as  described,  will  never  slide  if  properly 
constructed,  because  tho  number  and  size  of  the  tightening  bolts  can  be  calculated 
according  to  the  requisite  friction. 

Tho  unit  strain  of  60,000  pounds  per  square  inch  of  cable  wire  was  based  on  an 
ultimato  strength  of  180,000  pounds.  Much  stronger  wire,  up  to  300,000  pounds,  can 
be  made,  but  that  of  180,000  pounds  seems  preferable  on  account  of  its  easy  manu- 
facture and  cheap  price.  Tho  limit  of  elasticity  of  this  wire  is  120,000  to  130,000 
pounds,  hence  a  maximum  strain  of  60,000  pounds,  which  rarely  if  ever  occurs,  is  a 
perfectly  safe  assumption. 

The  stiffening  truss  is  subjected  to  reverse  strains,  hence  a  unit  strain  of  20,000 
pounds  per  square  inch  is  by  many  engineers  considered  equal  to  one  of  40,000 
pounds. 

Whilo  this  may  bo  true  if  the  opposito  strains  occur  in  rapid  succession,  namely, 
at  the  rate  of  5  to  20  and  more  times  per  second,  as  in  car  axles,  it  is,  on  tho  other 
hand,  known  from  the  experience  with  rails  and  continuous  bridges  that  it  is  not 
true  if  tho  interval  between  the  occurrence  of  tho  different  strains  within  the  clastic 
limit  affords  plenty  of  time  for  the  recovery  of  the  metal  from  the  elastic  deforma- 
tions. But  even  it  the  strains  were  as  high  as  40,000  pounds,  there  could  be  no 
objection  to  it  if  wre  adopt  high-grade  steel,  of  say  80,000  pounds  ultimate  strength 
and  50,000  pounds  elastic  limit,  considering  that  the  maximum  strain  in  the  stiffen- 
ing truss  is  based  on  an  improbable  assumption  of  load  distribution,  which  may  not 
occur  once  in  a  lifetime. 

Lastly,  it  may  bo  mentioned  in  justification  of  a  high  unit  strain,  that  the  stiffen- 
ing truss  is  not  a  necessity,  but  merely  a  convenience;  in  other  words,  it  could  bo 
dispensed  with  if  a  locomotive  and  train  could  ascend  a  6  or  8  per  cent  grade  ;  hence 
a  rupture  of  tho  truss  would  not  endanger  the  safety  of  tho  suspension  bridge,  but 
would  merely  cause  a  temporary  inconvenience. 

Tho  following  table  gives  the  calculated  weights  and  tho  approximate  cost  of  the 
bridge : 


Stiffening  trusses,  sway  braces,  and  intermediate  floor-beam  suspenders, 

11,190x3.100  =  17,345  tons  at  4  cents   $1,  387,  600 

Floor  construction,  4,200 X 3,200  =  6,720  tons  at  3£  cents   436,  800 

Towers,  26,330  tons  at  4  J  cents   2,  238,  000 

Anchor  chain  and  plates,  12,000  tons  at  3}  cents   840,000 

Woodwork  and  track,  5,200  pounds  at  $24    124,  800 

Cables,  12,000x5, 120  =  30,720  tons  at  7  cents   t,  300,  000 

Wind  cables  and  suspenders,  2,  350x3,200  =  3,760  tons  at  8  cents   601,  600 

East  land  span,  consisting  of  two  400-foot  span  truss  bridges,  weighing 

per  foot,  including  floor,  13,950  pounds X 800  =5,580  tons  at  4  cents   446,  100 

One  land  pier,  146  feet  high,  416  tons  at  4  cents   33,  300 

West  land  span,  consisting  of  three  266-foot  span  truss  bridges,  weigh- 
in--  per  foot,  including  floor,  9,000  pounds X 800  =  3,600  tons  at  4  cents.  288,  000 

Two  laud  piers,  146  feet  high,  468  tons  at  4  cents   38,000 

Anchorages   2,  500,  000 


Total,  106,959  tons  .   13,  234,  500 


This  is  without  the  cost  of  foundations.  In  explanation  of  the  cost  of  the  anchor 
ges,  it  may  bo  said  that  tho  cables  wero  assumed  to  be  anchored  in  rock  for  a  depth 
of  90  feet,  and  that  tho  masonry  above  the  rock  would  rise  142  feet  above  high 


68 


BRIDGE  ACROSS  THE  HUDSON  RIVER 


water.  For  each  anchorage  a  15  by  20  foot  shaft  is  supposed  to  be  sunk  in  the  rock, 
widened  at  the  bottom  to  50  by  50,  requiring  about  3,500  cubic  yards  of  excavation 
and  subsequent  tilling  with  concrete.  The  resistance  of  the  rock  body  surrounding 
two  of  these  shafts  is  at  least  72,000  tons,  and  if  a  block  of  masonry  containing  74,000 
yards  be  added  to  it  the  total  resistance  will  be  220,000  tons,  against  a  maximum 
pull  of  104,600  tons  in  the  cables.  Assuming  the  cost  of  excavation  at  $3  per  cubic 
yard,  filling  with  concrete  at  $6,  and  masonry  at  $14,  the  total  cost  of  both  anchor- 
ages will  be  $2,198,000,  or  $2,500,000,  allowing  15  per  cent  for  contingencies. 

The  cost  of  making  the  Brooklyn  bridge  cables  was  2.05  cents  per  pound.  Wire 
of  the  described  quality  can  be  bought  at  4  or,  at  the  outside,  4£  cents;  hence,  a 
price  of  6  to  6^  cents  per  pound  for  the  finished  cable  would  be  about  correct,  while 
1  cents  was  assumed  in  the  estimate  of  cost. 

The  estimate  must  be  considered  as  a  liberal  one  in  all  items. 

It  has  been  mentioned  that  cables  placed  vertically  over  each  other  may  be  con- 
nected in  a  way  to  form  a  suspended  arch.  This  requires  but  little  material  for 
stiffening  purposes.  No  advantage  was  taken  of  this  circumstance,  though,  if 
adopted,  it  would  considerably  lighten  the  weight  of  the  bridge. 

Another  reduction  in  the  weight  of  the  stiffening  girder  could  be  made  by  omitting 
the  center  hinge  and  making  the  truss  continuous.  This  would  reduce  its  weight 
nearly  10  per  cent,  but  as  the  calculation  of  such  a  truss  requires  the  introduction  of 
the  elastic  line,  and  could  not  be  checked  without  considerable  labor,  I  refrained 
from  discussing  the  same  in  this  communication. 

A  comparison  between  a  suspension  bridge  and  the  proposed  cantilever  bridge 
must  principally  refer  to  the  cost.  Assuming  the  weight  of  the  cantilever  bridge  to 
bo  about  116,000  tons,  its  cost  at  4  cents  per  pound  would  be  $9,280,000.  To  this 
must  be  added  the  cost  of  1,080-foot  approach,  because  the  suspension  bridge  is  so 
much  longer  from  end  to  end.  If  constructed  like  the  western  land  span,  this  cost 
would  amount  to  $440,000. 

It  appears  from  the  published  river  profile  that  the  foundation  of  the  west  canti- 
lever tower  must  reach  to  200  feet  below  water  level,  while  that  of  the  suspension 
bridge  tovrer  would  probably  be  less  than  100  feet.  This  would  make  a  difference 
of  at  least  $1,000,000  in  favor  of  the  suspension  bridge  if  the  lower  portion  of  the 
foundation  were  calculated  at  the  same  rate  of  cost  as  the  upper  portion.  The  end 
abutments  of  the  cantilever  bridge  will  add  $105,000,  hence  its  total  cost  (exclusive 
of  foundations),  as  compared  with  the  cost  of  a  3,200-foot  span,  will  be  $tf,280,000  -f 
$440, 000  -f  $1,000, 000  -f  $105, 000  =  $10,825, 000,  or  $2,409,500  less  than  a  suspension 
bridge  of  3,200-foot  span,  supposing  that  the  assumed  weight  of  the  cantilever  bridge 
be  approximately  correct. 

There  are  some  points  tending  to  lower  the  cost  of  the  suspension  bridge  or  to 
raise  that  of  the  cantilever,  for  instance,  the  erection  of  a  suspension  bridge  after 
the  cables  are  finished,  is  much  simpler  and  cheaper  than  the  erection  of  a  cantilever. 
The  latter  requires  two  false  works  810  feet  long  by  150  feet  high,  and  the  main 
span  must  be  erected  from  the  towers  toward  the  middle,  while  the  superstructure 
of  a  suspension  bridge  can,  without  false  works,  be  erected  simultaneously  at  many 
places,  as  the  cables  form  a  bridge  in  themselves  to  work  from  at  any  point. 

In  regard  to  the  safety  factor,  if  assumed  to  be  3  in  either  design,  it  is  relatively 
of  greater  value  for  the  suspension  cables  than  for  the  cantilever  truss,  because  the 
latter  is  exposed  to  impacts  while  the  cable  is  free  from  them.  A  rolling  load  of 
18,000  pounds,  on  which  the  calculation  of  the  suspension  bridge  was  based,  is  an 
excessive  assumption,  because  the  probability  of  a  fully  loaded  floor  decreases  pro- 
portionately w  ith  the  length. 

For  a  live  load  of  18,000  pounds  per  linear  foot  of  bridge  on  a  2,100-foot  span,  one 
of  15,000  pounds  per  linear  foot  would  be  a  full  equivalent  for  a  span  one-half  longer. 
This  item  alone  would  save  $226,000  in  the  cost  of  cables  and  anchor  chains,  not  to 
mention  the  saving  in  the  stiffening  trusses  and  anchorages. 

It  should  be  noticed,  also,  that  the  estimated  cost  of  the  suspension  bridge  includes 
contingencies,  while  no  contingences  were  considered  in  the  estimate  of  the  canti- 
lever. All  these  points  taken  into  consideration,  it  is  probable  that  the  actual  dif- 
ference of  cost  between  a  cantilever  bridge  of  2,100-foot  span,  resting  on  a  pier  in 
the  middle  of  the  river,  and  a  suspension  bridge  of  3,200-foot  span,  without  an  inter- 
mediate pier,  may  not  exceed  $2,000,000. 

In  the  foregoing  description  I  frequently  used  technical  terms  and  mathematical 
expressions  which  are  probably  of  no  interest  to  you,  but  as  I  understand  that  your 
object  is  to  submit  this  report  to  a  board  of  expert  engineers,  familiar  with  the 
science  of  bridge  construction,  I  know  they  will  find  it  easier  to  pass  an  opinion  on 
what  I  have  endeavored  to  elucidate  when  the  principles  from  which  the  data  were 
deduced  are  mentioned  than  if  I  had  merely  furnished  a  table  of  quantities. 

Respectfully  submitted, 

W.  HlLDENBKAND. 

Gustav  H.  Schwab,  Esq., 

Chairman  Special  Committee  Chamber  of  Commerce. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


69 


APPENDIX. — CALCULATION  OF  WIND  BRACING. 

Iii  addition  to  the  lateral  system  between  the  trusses  two  storm  cables  will  be 
stretched  under  the  tloor  from  tower  to  tower : 


These  cables  should  be  adjusted  to  a  bearing,  without  initial  strains,  at  110°.  The 
contraction  of  the  wire  at  zero  will  cause  an  initial  strain  of  20,800  pounds  per 
square  inch,  hence  the  strain  in  the  cables  will  be  a  maximum  if  the  greatest  wind 
would  occur  at  the  coldest  weather. 

If  it  be  the  strain  per  square  inch  of  cable  caused  by  the  wind  pressure,  the  total 

strain  in  the  cable  resisting  the  wind  force  will  be  very  nearly  20,800  -f-  ^an(1  *n  tne 

other  cable  20,800—  — , hence  if  t  =  2  X  26,800  pounds,  the  strain  in  one  cable  will  be 

53,600  pounds  per  square  inch,  and  in  the  other  0. 

Assuming  150  feet  to  be  the  deflection  of  the  cables  in  their  normal  position,  and 
allowing  an  extreme  side  deflection  of  the  floor  of  10  feet,  the  following  table  gives 
the  conditions  of  the  cables  at  0°  F. : 


Length  of 
cafle. 

Deflection. 

Tension 
per  square 
iueh. 

Pressure  per 
linear  foot 
of  span, pro- 
ducing the 
tension  per 
square  inch 
in  the  preced- 
ing column. 

Total  pres- 
sure tor 
entire  span. 

Feet. 

3215.  76 
3218.6 
3221.  4 

3216.  28 

Feet. 

Pounds. 

Pounds. 

Pounds. 

150 
160 

uo 

26,  800 
52, 600 
4,  220 

3. 14 
6.16 
0.5 

10,  048 
19,  712 
1,600 

It  follows,  from  these  figures,  that  a  strain  of  52,600  pounds  per  square  inch  for  a 
side  deflection  of  10  feet  from  the  normal  position,  will  resist  a  wind  pressure  of 
6.16  —  0.5  =  5.66  pounds  per  linear  foot  because  the  0.5  pound  arises  from  the  pressure 
of  the  opposite  cable,  and  not  from  the  wind,  or  a  total  pressure  of  18,112  pounds. 

The  wind  surface  was  approximated  at  42.5  square  feet  per  linear  foot,  and  the 
wind  pressure  at  30  pounds  per  linear  foot;  hence,  the  total  pressure  is  1,275  pounds 
per  linear  foot  extended  over  the  whole  middle  span.  Assuming  a  storm  cable  of 
126  square  inches  section  weighing  420  per  foot,  it  will  resist  a  pressure  of  126  X 
5.66  =713  pounds;  hence,  the  truss  chords  and  lateral  system  must  resist  1,275  — 
713=562  pounds  per  linear  foot. 

The  weight  of  the  horizontal-web  system  was  computed  at  434  pounds  per  linear 
foot.    The  chord  section  for  the  wind  truss  will,  therefore,  be  337  square  inches. 

The  deflection  (at  20,000  pounds  per  square  inch  unit  strain)  of  this  wind  truss  in 
the  plane  of  the  floor  beam,  and  assumed  as  continuous,  if  calculated  for  a  load  of 
562  pounds  per  linear  foot,  is  greater  than  10  feet;  hence,vthe  chord  section  must  bo 
increased  to  reduce  the  deflection  to  10  feet.  It  will  be  found  that  a  chord  section 
of  466  square  inches  per  truss  complies  with  this  condition,  which  reduces  the  unit 
wind  strain  from  20,000  to  14,000  pounds  per  square  inch. 

On  account  of  the  center  hinge  (hinging  the  truss  vertically)  it  will  be  necessary 
to  transmit  the  wind  pressure  to  the  towers  by  means  of  the  bottom  chord  alone. 
The  section  of  one  bottom  chord  of  each  of  the  two  trusses  in  the  quarter  span  ia 


70 


BRIDGE  ACROSS  THE  HUDSON  RIVLR. 


633  square  inches,  and  in  the  center  of  the  bridge  will  be  about  270  square  inches; 
hence,  it  will  be  necessary  to  add  196  square  inches  extending  over  about  300  feet 
each  side  from  the  center. 

The  wind  strain  in  the  quarter  span  will  be  found  to  be  2,585  tons.  This  is  resisted 
by  a  bottom-chord  section  of  633  square  inches  in  each  truss,  to  which  should  be 
added  53  square  inches  extending  over  700  feet  on  each  side  of  the  center.  With 
this  increase  of  section,  the  maximum  unit  strain  in  the  bottom  chord  would  be 
26,000  pounds,  under  the  supposition  of  the  improbable  case  that  the  greatest  wind 
strain  would  coincide  with  the  maximum  vertical  distortion  of  the  truss  under  a 
one-sided  load.  The  .additional  weight,  corresponding  to  the  mentioned  increase  of 
section  in  the  bottom  chord,  amounts  to  418  pounds  per  linear  foot  of  bridge. 

The  floor  beams,  which  are  supposed  to  bo  30  feet  apart,  must  resist  the  pressure 
of  tbo  cables,  amounting, to  126x6.16  =  776  pounds  per  linear  foot,  or  of  23,280  pounds 
per  floor  beam.  This  will  require  an  increase  of  1.16  square  inches,  or  370  pounds 
of  metal  per  floor  beam,  equal  to  13  pounds  per  linear  foot. 

The  total  weight  of  the  wind  system,  therefore,  is : 

Pounds  per 
linear  foot. 


Lateral- web  system   434 

Additional  of  bottom  chords  of  trusses   418 

Increase  in  floor  beams   13 

Storm  cables   840 


Total   1,705 


In  the  original  estimate  of  weight  the  total  weight  of  wind  bracing  was  calculated 
to  be  1,240  pounds  per  linear  foot,  based  on  the  supposition  of  a  continuous  truss 
which  could  transmit  the  wind  pressure  to  the  towers  without  requiring  additional 
chord  sections. 

The  suspender  weight  was  calculated  for  a  unit  strain  of  20,000  pounds,  while 
40,000  pounds  would  be  a  moderate  strain  if  the  suspenders  be  constructed  of  wire 
rope,  reducing  the  assumed  weight  one-half. 

The  weight  of  wind  bracing  a*nd  suspenders  should  therefore  be  corrected  as  follows : 

1,705  +  555  =  2,260  lbs.,  costing  865  lbs.  X  3,100  1,340  tons,  at  4  cents  =  $107,260 

840  +  555=1,395  lbs.  X  3,200  2^232  tons,  at  8  ceuts=  357^120 

3,572  464,380 

This  is  188  tons  and  $137,000  less  than  given  in  the  estimate  on  page  67. 

The  tower  columns  were  calculated  for  a  unit  strain  of  12  tons  on  top  and  10  tons 
at  the  bottom ;  hence,  no  addition  was  made  for  wind  strains,  which  are  insignificant 
compared  with  the  direct  strains  from  the  weight  of  the  bridge. 

W.  HlLDENBRAND. 


Appendix  C2. 

STATEMENT  OF  MR.  W.  HlLDENBRAND  TO  THE  BOARD  OF  ENGINEERS. 

New  York,  July  20,  1S94. 
Gentlemen:  I  beg  to  submit  to  you  herewith  a  modified  plan  and  estimate  for  a 
suspension  bridge  across  the  Hudson  River  at  Sixtieth  street.  It  differs  from  my 
former  design,  offered  to  the  inspection  of  your  honorable  Board  on  .July  17  by  the 
chairman  of  the  special  committee  of  the  Chamber  of  Commerce,  in  being  adapted 
to  the  correct  profile  of  the  river  and  complying  with  your  instructions  as  to  unit 
strains  in  different  parts  of  the  superstructure  and  the  admissiblo  pressure  on  the 
foundation : 

The  following  are  the  principal  data  of  this*  plan: 


Total  length  of  bridge  feet..  4,  310 

Span  from  ceiiter  to  center  of  towers  do. 3,  310 

Width  of  towers  at  base  do . . .  180 

Clear,  span  between  piers  (=elear  waterway  between  pierhead  lines). do. 3.  130 

Width  of  tower  at  high  water,  center  to  center  of  columns  do. 131.5 

Length  of  tower  at  high  water,  center  to  center  of  columns  do. 340 

Width  of.  tower  at  floor  line  do. . .  100 

Wi (1 1  li  of  tower  at  top  do. ..  70 

Clear  span  of  cable  in  middle  span  do. . .  3,  240 

1  Reflection  of  cable  at  55°  F  do . .  .  400 

1  )ellection  of  cable  at  0°  F  do. . .     397.  63 

1  Reflection  of  cable  at  110°  F  do. . .     402.  30 

Lengths  of  cable  in  center  span  at  55°  do. ...  3, 369. 1 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


71 


do...  0.3 


Lengths  of  west  back  cable  feet . .  1, 611. 7 

Lengths  of  east  back  cable  do . . .      903.  2 

Total  lengths  of  cable,  anchorage  to  anchorage  do. . .  5,  884 

Rise  and  fall  of  cable  for  a  difference  of  temperature  of  from  ()°-110o . .  .do. . .        4. 67 
Deflection  of  west  back  cable  from  a  straight  line  connecting  top  of  tower 
and  anchor  pin : 

For  dead  load  feet. .       32. 1 

For  dead  and  live  load  do.  21.  6 

Deflection  of  east  back  cable  from  a  straight  line  connecting  top  of  tower 
and  face  of  anchorage  : 

For  dead  load  feet . .  8 

For  dead  and  live  load  do . . .         5.  3 

Depression  of  center  span  when  fully  loaded  arising — 

Feet. 

From  elongation  of  center  cable   1.77~ 

From  elongation  of  west  back  cable   0.  85 

From  elongation  of  east  back  cable   0.47 

From  change  of  deflection  in  west  back  cable,  causing  the 

saddle  to  move  forward   0.  92 

The  same  of  the  east  back  (  able   0.  06  J 

(This  depression  could  be  reduced  one-half  if  the  cables  wrere  connected 

with  the  land  piers  by  suspenders  and  held  down.) 
Total  rise  and  fall  in  center  of  bridge  under  extremes  of  temperatures  and 

loads  ,  feet..  10.97 

Camber  of  floor  at  55°  F  do. .  .  9 

Grade  of  floor  at  55°  F  per  cent. .        1. 11 

Gradeof  llooratO°F.  (camber  11.37  ,  less  contraction  of  tower  =  0.19). do. . .  1.38 
Grade  of  floor  at  1103  F.  (camber —  6.7 -f  elongation  of  tower  =  0. 19). do. ..  0.85 
Camber  of  floor  at  110°  if  fully  loaded  (0.4  -f-  elongation  of  tower) . .  .feet. .        0. 59 

These  figures  show  that  the  floor  will  never  sink  below  level  and  that  the  maximum 
grade  is  less  than  H  per  cent.  It  should  also  be  noticed  that  this  grade  extends 
only  over  a  few  feet  near  the  towers,  and  diminishes  rapidly  when  a  train  proceeds 
toward  the  center  of  the  bridge. 

The  height  of  the  towers  is : 

Feet. 

From  high  water  to  under  side  of  bridge   150 

Thickness  of  floor   8 

Camber  of  floor  #.   9 

Bottom  of  cable  above  floor   2 

Deflection  of  cable  at  55°   400 

Extra  height  for  the  support  of  two  tiers  of  cables   40 

Total   589 

The  live  load  was  assumed  to  be  18,000  pounds  per  linear  foot.  The  unit  strain  in 
stiffening  trusses  does  not  exceed  15,000  per  square  inch  for  reversed  stresses.  The 
unit  strain  in  the  cables  was  restricted  to  50,000  pounds  per  square  inch  for  wire 
having  an  ultimate  strength  of  180,000  pounds.  The  stiffening  truss  was  calculated 
to  resist  a  live  load  of  18,000  pounds  per  linear  foot,  covering  one-half  of  the  span, 
while  the  opposite  half  be  unloaded. 

It  will  require  a  moving  load  of  2,400  pounds  per  linear  foot  to  deflect  the  dead 
mass  of  the  bridge  (without  regard  to  any  stiffening)  3.8  feet  in  one-quarter  span 
and  raise  it  3.7  feet  in  the  opposite  quarter. 

This  distortion  of  the  floor  causes  a  grade  of  less  than  1  per  cent.  Hence  this 
stiffening  girder  was  calculated  for  a  moving  load  of  15,000  pounds. 

To  comply  with  this  condition  and  not  to  strain  the  metal  above  15,000  pounds  per 
square  inch,  the  height  of  the  truss  was  chosen  to  be  120  feet  giving  the  following- 
dimensions  : 

Maximum  chord,  section  of  either  top  or  bottom  chords  square  inches.  1,  395 

Average  weight  of  both  chords  pounds  per  linear  foot.  8,000 

Average  weight  of  web  svtem  do  4,220 


Total  do  ....12,280 

It  will  be  found  that  the  deflection  of  this  truss  for  a  load  of  15,000  pounds  per 
linear  foot  is  2.35  feet  if  the  elongations  and  contractions  of  the  web  members  be 
neglected;  hence  its  true  deflection  will  about  coincide  with  the  distortion  of  the 
cable  under  a  load  of  2,400  pounds  per  linear  foot. 


72 


BRIDGE  ACROSS  THE  HUDSON  RIVE1?. 


The  intermediate  floor-beam  suspenders  and  cross-bracings  were  calculated  for  a 
local  load  of  200  tons,  in  addition  to  the  dead  weight  on  each  suspender. 


<        30         X        30         X        30  > 


I  I  I  I  I  T     T     T  T     I     T     T      T  T 


T  T 

20$  t.  209  t. 


Allowing  a  unit  strain  of  20,000  pounds  per  square  inch,  the  weight  of  these  parts 
will  be  1,332  pounds  per  linear  foot. 

The  question  was  investigated  whether  there  was  an  appreciable  inclination  of 
the  floor  beams  if  three  tracks  on  one  side  of  the  axis  of  the  bridge  were  fully 
loaded  in. one-half  of  the  spans,  and  if  the  opposite  three  tracks  were  loaded  in  the 
other  half  of  *<4io  span.  For  instance,  a  load  of  9,000  pounds  per  linear  foot  on  the 
three  right-hand  tracks  will  depress  the  right  end  of  the  floor  beams  1.37  feet  and 
the  left  end  0.53  foot.  The  same  load  on  the  left  three  tracks  in  the  opposite  half 
span  will  raise  the  right  ends  of  the  former  floor  beams  0.53  foot,  and  will  depress 
the  left  ends  1.35  feet;  hence,  the  greatest  inclination  of  a  floor  beam  is  1.68  feet  in 
100  feet,  which  is  hardly  noticeable. 

The  two  suspenders  of  one  floor  beam  wore  calculated  with  a  unit  strain  of  50,000 
pounds  per  square  inch  for  the  dead  load,  plus  600  tons,  assuming  six  100-ton  loco- 
motives to  meet  on  one  floor  beam. 

The  estimated  weight  is  776  pounds  per  linear  foot.  The  aggregate  load  to  be  sus- 
tained by  the  cable  is : 

Pounds  per 
linear  foot. 


Moving  load   18.000 

Stiffening  trusses   12,  280 

Platform   5,400 

Projecting  ends  of  floor  beams   300 

Intermediate  floor-beam  suspenders  and  sway  braces   1,  340 

Lateral  wind  bracing   860 

Storm  cables   840 

Suependers   780 

Cables   13,000 


52,  800 

Total  load  on  cables,  39,  800x3,210  +  13,000x3,240=84,939  tons. 
Tension  in  cable  at  one-eighth  deflection,  94,960  tons. 

Allowing  25  tons  strain  per  square  inch,  it  requires  3,800  square  inches,  or  81,270 
No.  3  wires  (0.244  inch  diameter). 

Dividing  the  number  of  wires  into  16  cables,  one  cable  will  contain  5,080  wires 
and  will  have  a  diameter  of  20|  inches. 

The  tension  in  the  east  anchor  chain  will  bo  94,700  tone.  The  tension  in  the 
west  anchor  chain  will  be  88,500  tons;  average  tension,  91,600  tons;  requiring  9,160 
square  inches  and  weighing  39,700  pounds  per  linear  foot. 

Tons. 

Total  weight  of  anchor  chain  for  a  length  of  510  feet   10, 120 

Weight  of  anchor  plates   1,  580 


11,  700 


BRIDGE  ACROSS  THE  HUDSON"  RIVER.  73 

The  towers  were  calculated  for  the  combined  maximum  load  and  wind  strains  at 
12  tons  per  square  inch. 

Tons. 

Weight  on  top  of  tower  (requiring  7,080  square  inches)   84,940 

Weight  of  tower   15, 110 

Weight  of  land  truss  resting  on  tower   1,  400 

Wind  strains   1,  350 

Pressure  at  base  of  tower,  102,800  tons,  requiring  8,566  square  inches.  Average 
section,  7,823  square  inches. 

Weight  per  linear  foot,  52,150  pounds. 
Total  weight  of  two  towers,  579  feet  high,  30,200  tons. 


The  pressure  on  the  rock  foundation  of  the  east  tower  will  be  247,380  tons,  and 
the  buoyancy  of  the  pier  cylinder  90,250;  hence  the  foundation  must  contain  15,713 
square  feet  in  order  to  resist  a  pressure  of  157,130  tons. 

This  area  can  be  procured  by  sinking  eight  cylinders  of  50  feet  diameter,  filled 
with  concrete,  one  for  each  tower  column.  The  total  mass  of  foundation  work  will 
amount  to  2,081,300'cubic  feet.  The  pressure  on  the  west  tower  is  less,  owing  to  the 
light  inclination  of  the  back  cable,  hence  concrete-filled  cylinders  of  47  feet  diame- 
ter will  answer  the  conditions  of  the  foundation. 

The  total  pressure  is  137,710  tons,  requiring  a  foundation  mass  of  1,958,600  cubic 
feet. 

The  east  land  pier,  supporting  two  independent  400-foot  truss  bridges,  requires  a 
foundation  mass  of  100,400  cubic  feet,  requiring  four  cylinders  of  20  feet  diameter. 
As  regards  the  pressure  on  the  foundation,  the  cylinders  might  be  smaller,  but  as 
they  must  be  sunk  to  a  depth  of  about  80  feet,  a  smaller  diameter  seems  not  to  be 
advisable.  No  land  spans  were  designed  for  the  west  side,  as  the  west  tower  coin- 
cides with  the  position  of  the  west  end  abutment  of  the  cantilever  bridge;  hence, 
whatever  construction  be  used  for  this  approach  would  be  common  for  both  designs. 

The  west  anchorage  is  entirely  in  rock  200  feet  below  the  surface,  requiring  13,200 
cubic  yards  of  rock  excavation,  9,000  cubic  yards  of  concrete  filling,  and  25,000 
cubic  yards  of  masonry. 

Estimating  the  rock  excavation  at  $4,  the  filling  at  $6,  and  the  masonry  at  $14  per 
cubic  yard,  the  cost  of  this  anchorage  will  be  $456,000. 

The  east  anchorage  is  also  partially  in  rock,  which  according  to  the  contour  of 
the  rock  strata  will  probably  be  found  at  a  depth  of  30  to  35  feet  below  high  water. 
It  requires,  therefore,  6,800  cubic  yards  of  rock  excavation  and  filling,  80,000  cubic 
yards  of  earth  excavation,  and  80,000  cubic  yards  of  masonry. 

Estimating  rock  excavation  at  $3,  earth  excavation  at  50  cents,  concrete  filling  at 
$6,  and  masonry  at  $14,  the  cost  of  this  anchorage  will  be  $1,221,000. 

The  following  is  the  calculated  weight  and  estimated  cost  of  the  bridge: 


Stiffening  truss,  12,280  x  3,210=  19,710  tons  at  4  cents   $1,  576.  700 

Platform,  4,200  x  3,310=6,950  tons,  at  3£  cents   451,  800 

Intermediate  floor-beam  suspenders  and  sway  bracing,  1,340x3,210  = 

2,150  tons,  at  4  cents   172.  000 

Towers,  30,200  tons,  at  4£  cents   2,  576,  000 

Woodwork  and  track,  4,310  feet,  at  $24   103,  400 

Anchor  chains  and  plates,  11,700  tons,  at  3^-  cents   81!>.  000 

Cables,  13,000  X  5,884  =  38,250  tons,  at  7  cents   5, 354, 400 

Wind  laterals  and  additional  weight  in  bottom  chord  and  floor  beams, 

860  X  3,210  =  1,380  tons,  at  4  cents   110,  400 

Storm  cables,  840  X  3,210  =  1,350  tons,  at  8  cents   235,  700 

Suspenders,  780  X  3,210=  1,250  tons,  at  8  cents   200.  300 

East  land  span,  13,950  X  800  =  5,580  tons,  at  4  cents   446.  400 

East  land  pier,  150  feet  high  =420  tons,  at  4  cents   33,  600 

Anchorages   1,  760,  000 


Total  superstructure,  118,940  tons   13,  830,  700 

Total  foundation  mass  =  4,140,000  cubic  feet,  estimated  at  50  cents,  will 

amount  to   2,  070.  000 


Total  bridge,  4,310  feet  long   15,  900,  700 


The  proposed  cantilever  bridge  is  but  4,120  feet  long,  and  if  its  weight,  as  assumed 
in  my  former  report  be  correct,  and  the  foundation  be  calculated  on  the  same  basis, 
its  cost  would  be  about  $12,665,000,  or  $3,235,000  less  than  a  single  span  suspension 
bridge. 

If  the  cantilever  bridge  was  calculated,  as  I  understand  it  was,  for  a  unit  strain 
of  20,000  pounds  per  square  inch  of  metal,  I  beg  to  draw  the  attention  of  your  hon- 
orable Board  to  the  fact  that  this  circumstance  puts  the  comparison  between  the  two 


74 


BRIDGE  ACROSS  THE  HUDSON  RIVEu. 


bridges  on  two  different  bases.  According  to  Cooper's  specifications,  soft  steel  would 
not  reach  a  strength  of  over  60,000  per  square  inch,  and  medium  steel  would  have 
an  average  strength  of  64,000  pounds,  hence  a  strain  of  20,000  per  square  inch 
is  equal  to  a  factor  of  not  over  3.2.  The  steel  wire  of  which  the  cables  of  the  suspen- 
sion bridge  are  to  be  made  will  have  a  minimum  strength  of  180,000  pounds,  hence 
a  unit  strain  of  50,000  pounds  is  equal  to  a  safety  factor  of  3.6.  If  this  factor  be 
placed  at  only  3.2,  as  in  the  cantilever  bridge,  the  admissible  unit  strain  would  be 
56,000  pounds  and  the  saving  in  the  cost  of  cables  $600,000,  and  in  towers  and 
anchorages  $180,000. 

In  regard  to  employing  a  unit  strain  of  20,000  pounds  for  the  stiffening  truss,  as 
assumed  in  my  first  report,  it  seems  at  lirst  sight  high  on  account  of  working  in 
compression  as  well  as  in  tension,  which  induced  your  honorable  Board  to  restrict 
this  strain  to  15,000  pounds  per  square  inch.  Personally  I  believe  that  a  strain  of 
20,000  will  give  ample  safety,  because  the  reverse  strains  will  occur  only  at  long 
intervals.  But  even  with  a  strain  of  15,000  the  weight  of  the  stiffening  construction 
could  easily  be  reduced  1,800  to  2,000  pounds  per  linear  foot  by  connecting  each  pair  of 
cables  in  a  vertical  plane  in  a  way  to  form  a  suspended  arch.  The  saving  of  weight 
in  the  superstructure,  cables,  towers,  anchorages,  and  foundation  work  would,  in  that 
case,  amount  to  at  least  $1,600,000,  reducing  the  difference  of  cost  between  the  two 
designs,  cantilever  and  suspension  bridge,  to  about  $1,500,000. 

Respectfully  submittted. 

W.  HlLDENBRAND. 

To  the  Board  op  Engineers, 

New  Yorlc  and  New  Jersey  Bridge. 


Appendix  D. 

NORTH  RIVER  BRIDGE  TO  HOBOKEN. 
[Designed  by  G.  Lindenthal,  Chief  Engineer.] 
GENERAL. 

Location. — It  is  shown  on  the  attached  map,  Exhibit  A.  Under  the  charter  the 
company  could  locate  the  bridge  anywhere  over  the  Hudson  River  between  the  Bat- 
tery and  the  northern  New  York  City  limit.  The  location  at  Hoboken  was  advised 
by  the  principal  railroad  interests  as  the  most  direct  entrance  into  New  York.  It 
has  also  the  advantage  of  accommodating  local  travel  to  Hoboken  and  Jersey  City 
Heights,  the  revenue  from  which  will  be  a  large  item. 

From  a  purely  engineering  point  of  view  a  location  farther  up,  where  the  rocky 
bluffs  are  close  to  the  water's  edge,  would  have  been  preferable.  It  would  have 
cheapened  the  construction  of  the  bridge  (with  a  single  span  under  the  charter)  by 
several  million  dollars.  The  managers  of  the  company,  however,  considered  the 
business  advantages  of  locating  at  Hoboken,  and  the  larger  revenue  therefrom  as 
far  outweighing  the  cheaper  cost  of  construction  on  a  location  farther  north. 

The  location  was  approved  by  the  Secretary  of  War  December  29, 1891. 

The  New  York  anchorage  for  this  location  had  to  bo  placed  at  the  intersection  of 
Twenty-third  street  and  Tenth  avenue,  where  the  borings  indicated  the  rock  at  22 
feet  below  the  surface.  It  is  the  old.  natural  river  shore.  From  this  line  towards 
the  river  is  made  ground,  and  the  rock  dips  rapidly,  reaching  a  depth  of  190  feet  at 
the  foot  of  Twenty-second  street,  where  the  New  York  tower  is  located. 

Rocky  bottom  (whether  solid  or  bowlders  is  not  definitely  known  yet),  overlaid 
with  sandy  clay,  containing  smaller  bowlders  to  a  depth  of  26  feet,  is  found  to  exist 
for  the  New  Jersey  anchorage.  The  New  Jersey  tower  will  require  less  than  one- 
half  the  depth  of  the  New  York  tower  for  a  foundation. 

The  river  between  pierhead  lines  is  here  2,740  feet  wide.  The  New  Jersey  tower 
is  located  close  to  the  New  Jersey  pierhead  line.  The  New  York  tower  is  located 
150  feet  back  of  the  New  York  pierhead  line,  to  shorten  the  New  York  end  span, 
and  to  avoid.deoper  foundations.  The  resulting  span  is  3,100  feet  center  to  center 
of  towers. 

The  total  length  of  the  bridge  between  anchorages  is  6,800,  and  including  the 
anchorages,  7,340  feet. 

Capacity  of  bridge. — It  is  based  on  tho  view  that  the  bridge  must  derive  its  largest 
business  from  suburban  traffic  at  low  rates.  Tho  passenger  travel  to  distant  points, 
together  with  the  freight  traffic  likely  to  go  over  the  bridge,  would  not  pay  on  the 
investment. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


75 


The  bridge,  as  a  lateral  outlet  for  the  masses,  must  have  a  largo  track  capacity, 
on  which  the  company  has  been  at  great  pains  to  get  the  advice  and  estimates  of, 
railroad  managers  familiar  with  the  situation. 

It  is  not  necessary  to  give  here  the  estimate  of  the  number  of  trains  capable  of 
handling  over  the  bridge,  but  only  to  explain  that  the  in  and  out  going  tracks  will 
be  connected  by  loops  at  the  New  York  terminus  to  avoid  switching  and  delay,  and 
to  save  the  costly  space  for  a  switching  station.  As  far  as  the  Now  York  passenger 
terminus  is  concerned,  it  will  be  as  for  a  4-track  railroad  doubled  on  itself. 

A  switching  and  cleaning  yard  will  bo  provided  in  the  New  Jersey  meadows. 

The  number  of  tracks  over  the  bridge  will  be  8,  namely,  2  tracks  for  suburban 
tra  vel,  2  tracks  for  through  passenger  and  express  trains,  2  tracks  for  freight,  and  2 
tracks  for  electrical  railroads. 

During  certain  hours  in  the  morning  and  evening  the  freight  tracks  will  be  avail- 
able also  for  suburban  business. 

The  suburban  loaded  trains  coming  in  the  morning  will  turn  around  the  loop  and 
go  back  empty  to  their  respective  yards.  The  reverse  process  will  take  place  in  the 
evening  hours. 

Since  the  largest  growth  of  business  will  come  from  the  suburban  traffic,  the 
structure  is  so  designed  as  to  permit  of  an  addition  of  6  rapid-transit  tracks  on  a 
second  deck. 

The  anchorages  and  towers  will  be  constructed  for  a  capacity  of  14  tracks,  as 
shown  below.  All  other  parts  of  the  structure  will  be  erected  for  a  capacity  of  8 
tracks. 

The  additional  cost  of  the  heavier  anchorages  and  towers  is  such  a  small  percent- 
age (about  9  per  cent)  of  the  total  cost  of  the  structure  that  it  cuts  no  figure  in  the 
large  cost  of  the  entire  undertaking. 

Following  is  a  brief  description  of  the  salient  features,  and  of  the  dimensions  and 
quantities  of  material  in  the  structure: 

(1)  Anchorages. — Pull  on  each  anchorage. 

From  dead  load,  8  tracks  (15  tons  per  linear  foot  of  superstructure),  58,000  tons. 
From  the  assumed  live  load  (12  tons  per  linear  foot  of  bridge  on  8  tracks),  46,000 
tons.    Total,  104,000  tons. 

Provision  is  made  for  a  future  increase  to  14  railroad  tracks,  for  which  the  pull 
from  dead  load  (19  tons  per  linear  foot  of  suspended  superstructure)  would  be  73,000 
tons,  and  for  live  load  (18  tons  per  linear  foot  of  bridge),  extreme  limit,  65,000  tons. 
Total,  138,000  tons,  maximum. 

Total  net  section  of  anchorage  steel  bars  (60,000  ultimate  average  strength)  in 
each  anchorage,  10,000  square  inches. 
# 

Anchor  platforms  of  steel,  90  feet  below  the  pavement. 

Weight  of  masonry  and  rock,  and  filling  of  stone,  gravel,  and  sand,  of  each 

anchorage  tons . .  480,  000 

Assumed  coefficient  of  friction  for  masonry  on  foundation   0.  60 

Minimum  resistance  of  anchorages  against  sliding  tons..  288,  000 

Total  bearing  area  of  anchor  platform  and  anchor  chains  against  masonry 

in  each  anchorage  ...  square  feet. .    17,  000 

(For  quantities,  see  estimate  below.) 

Quantities  in  each  anchorage  (to  grade  line). 

Excavation  cubic  yards. .    30,  000 

Concrete  masonry  do   96,  000 

Ashlar  granite  facing  cubic  feet. .  440,  000 

Filling  for  weight,  rock,  gravel,  sand,  and  tamped  earth  cubic  yards..  160,  000 

Steel  in  anchors  and  anchor  bars  tons..     6,  200 

Asphaltum  for  metal  bearings  cubic  feet..      1,  000 

Note. — The  structure  above  the  grade  line  of  the  anchorage  is  a  building  with  an 
open  court  or  yard  over  the  tracks— this  building  to  contain  way  station  (for  elec- 
trical cars),  accessible  by  elevators  from  the  street,  the  upper  part  to  contain  offices 
(for  renting  purposes)  with  their  windows  out  upon  the  inclosed  space  or  court. 

The  outside  of  this  building  corresponds  in  architecture  with  the  base  of  the 
anchorage,  but  the  weight  of  the  building  is  not  considered  (in  the  above  given 
weight)  as  a  part  of  the  anchorage. 

(2)  Towers. — The  tower  bases  are  hollow,  of  masonry,  reaching  40  feet  below  high 
water  and  extending  30  feet  above  high  water. 

The  construction  of  the  tower  foundation  on  New  Jersey  side,  90  feet  down  to  rock, 
is  by  the  usual  pneumatic  method,  using  a  wooden  caisson,  175  by  335  feet,  with 
two  hollow  spaces,  each  90  feet  square,  where  there  is  no  pressure  from  the  steel  col- 
umns, the  air  chamber,  after  reaching  firm  bearing,  to  be  filled  with  packed  sand  and 
gravel,  and  with  concrete  where  necessary. 


76 


BRIDGE  ACROSS  THE  HUDSON  RIVER 


The  wooden  caisson  is  of  cellular  construction;  one-third  of  the  section  consists 
of  gravel  and  sand  filling. 

Bearing  area,  40,000  square  feet. 

Pressure  on  foundation  80,000  tons  from  tower  base,  after  deducting  displacement; 
76,500  tons  superstructure  and  steel  tower,  complete  lor  14  tracks;  61,000  tons 


extreme  live  load  from  14  tracks;  total,  217,500  tons. 

Tons. 

Pressure,  per  square  foot   5.  425 

From  wind  pressure  of  3,000  tons  on  tower,  on  lee  side  200 


Maximum  (per  square  foot)   5.  625 

From  dead  load  alone  (per  square  foot)   3.  92 


Maximum  pressure  on  timber,  80  pounds  per  square  inch. 

The  New  York  tower  foundation,  190  feet  down  to  rock,  is  of  a  different  construc- 
tion. An  open,  braced  caisson,  or  cofferdam,  with  lower  edge  conforming  to  con- 
tour of  rock,  as  obtained  by  borings  all  around,  350  by  180  inside,  of  wood  and 
iron,  10  feet  thick,  filled  with  gravel,  is  first  sunk  and  the  inside  dredged  out  down 
to  rock,  which  is  leveled  off  with  concrete  in  bags,  and  finely  broken  stone,  below 
water  A  hollow-spaced  wooden  crib,  345  feet  by  175  feet  and  150  feet  deep,  is  built 
up  lioating  inside  the  caisson.  Two  large  hollow  spaces,  75  feet  square,  enlarging 
towards  the  top  to  90  feet  square,  are  spared  out  in  the  center  of  each  half  tower, 
where  there  is  no  pressure  from  the  steel  columns.  Masonry  below  water  is  also 
built  with  hollow  spaces.  The  whole  mass  of  foundation  is  calculated  to  iloat 
during  construction,  so  that  all  masonry  can  be  done  above  water  till  the  whole 
settles  down  evenly  upon  the  leveled  foundation.  All  hollow  spaces  in  the  wooden 
crib  are  then  tilled  with  gravel  and  sand,  and  in  the  masonry,  with  concrete. 

Maximum  pressure  on  rock  foundations:  New  York  tower,  130,000  tons,  tower 
base,  after  deducting  displacement;  75,000  tons,  superstructure  and  steel  tower; 
61,000  tons,  extreme  live  load.  Total  pressure,  267,500  tons  on  50,000  square  feet, or 
5.35  tons  per  square  foot;  from  extreme  wind  pressure,  0.26;  maximum  pressure, 
5.61  tons  per  square  foot;  from  dead  load  alone,  4.13  tons  per  square  foot;  maxi- 
mum pressure  on  timber,  80  pounds  per  square  inch. 

Each  steel  tower  has  16  columns,  with  a  total  cross  section  of  hard  steel  (100,000 
pounds  ultimate  per  square  inch*).  At  the  top,  16x515  square  inches  =^,240  square 
inches.    At  the  base,  16x580  square  inches— 9,280  square  inches. 

Diameter  of  columns,  8  feet  at  top;  9  feet  at  bottom. 

(For  quantities,  see  estimate  below.) 

Pounds. 


Compression  per  square  inch  of  steel  from  dead  load  of  only  8  tracks,  and 

from  maximum  bending  moment   12,  500 

From  maximum  live  load  of  only  8  tracks   9,  600 


Total   22, 100 


From  dead  load  in  the  future  of  14  tracks  and  from  maximum  bending 

moment   15,  300 

From  maximum  live  load  of  14  tracks   14, 400 


Possible  maximum  total   29,700 


The  elastic  limit  of  the  100,000  pound  steel  is  60,000  pounds.  Buckling  strength  of 
steel  columns  is  54,400  pounds  per  square  inch. 

With  16  trains  of  ordinary  size  (600  tons  each)  on  the  bridge,  the  total  compres- 
sion per  square  inch  in  the  tower  columns  will  not  exceed  13,500  pounds  per  square 
inch  for  8  tracks  superstructure. 

For  14  tracks  superstructure  the  total  compression  from  dead  and  live  load  will 
rarely  reach  17,000  pounds  per  square  inch. 

The  above  considered  maximum  compression  of  29,700  pounds  per  square  inch 
may  never  occur  in  the  life  of  the  bridge.  It  would  require  a  live  load  of  122,000 
tons,  equal  to  about  3,000  loaded  freight  cars. 

The  temperature  strains  in  the  cable  do  not  affect  the  towers,  but  the  towers 
themselves  are  exposed  to  bending  strains  from  temperature  differences  in  the  col- 
umns, exposed  to  the  heat  of  the  sun,  and  others  being  in  the  shade.  The  computed 
deflection  of  tower  tops  from  this  cause,  for  differences  of  30°  P.,  is  2  inches. 

The  deilection  of  tower  tops  lengthwise  with  bridge  from  difference  of  load  effects 
will  not  exceed  8.1  inches. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


77 


Quantities  in  Neiv  Jersey  tower  base  (00  feet  below  high  water). 

Excavation  cubic  yards. .  105,  000 

Timber  M . .  20,  000 

Irou  tons . .  460 

Concrete  below  water  cubic  yards..  3,000 

Gravel  and  sand  tilling  do   40,  000 

Masonry  of  hard-burned  brick. 

Concrete  and  granite  facing  and  coping  cubic  yards..  50,  000 

Quantities  in  Neiv  York  tower  base  and  cofferdam  (192  feet  below  high  water). 

Excavation  cubic  yards . .  3G0,  000 

Timber  M . .    65,  000 

Iron  tons..  2,340 

Concrete  under  water  cubic  yards. .      1,  000 

Broken  stone  do   3,  000 

Gravel  tilling  do   180,000 

Masonry,  tbo  same  as  for  other  tower  do   56,  000 

Weight  of  steel  for  each  tower: 

Sixteen  columns,  with  base  plates  and  cable  bearings  tons..    7,  220 

Lattice,  horizontal,  wind,  and  longitudinal  bracing  do . . .    4,  060 

Cable  chambers  on  top  and  upper  bracing  between  towers  do. . .  040 


One  tower  do.. .  12,220 

Two  towers  do. . .  24,  440 

Quantities  for  each  pedestal : 

Excavation  cubic  yards . .    2,  000 

Masonry,  concrete,  with  granite  facing  and  coping  do   1,  200 

Steel  columns,  with  bracing  and  vertical  anchorage  tons..  170 

(3)  Cables. — The  4  cables  are  computed  with  a  factor  of  safety  of  3  for  a  dead 
load  of  15  tons  per  linear  foot,  and  for  a  moving  load  of  12  tons  per  linear  foot, 
covering  the  entire  bridge.    Maximum  total  load,  27  tons  for  8  tracks. 

In  ordinary  operation  the  moving  load  will  rarely  reach  3,000  tons  for  the  middle 
span  on  all  8  tracks. 

The  4  cables  are  composed  of  pin-connected  wire  links.  Each  wire  link  is  made 
up  to  accurate  length  of  parallel  wires  looped  around  flanged  steel  shoes,  bored  out 
to  tit  the  pins.  The  pins  are  16  inches  diameter  and  hollow.  The  steel  wire  is 
No.  3,  Birmingham  gftuge  (0.259  diameter),  and  has  an  ultimate  strength  of  180,000 
pounds  per  square  inch  (9,600  pounds  per  wire). 

Wire  links  have  the  advantage  of  accurate  work  and  close  inspection  in  the  shop, 
quick  erection,  and  testing  to  destruction,  so  their  accurate  value  may  be  known. 
Wire  links  permit  also  of  variations  in  the  cable  section,  as  needed. 

The  length  of  the  wire  links  varies  from  50  feet  at  the  center  to  54  feet  at  the 
towers. 

The  horizontal  panel  length  is  50  feet  throughout. 

The  links  contain  from  400  to  800  wires  each,  according  to  position  in  the  cable, 
and  on  the  pins. 

The  vertical  distance  of  the  cables  is  55  feet  from  center  to  center  throughout, 
i.  e.,  the  upper  and  lower  cable  have  the  same  curvature. 

Each  cable  is  composed  of  3  chains,  one  above  the  other,  coupled  vertically  at 
the  pins.  The  vertical  couplings  consist  of  one-half  inch  steel  plates  between 
links,  sufficiently  strong  transversely  to  transmit  the  increment  of  the  web  strains 
into  the  chains  of  the  cable. 

The  middle  chain  has  alternately  9  and  10  links,  and  the  upper  and  lower  chains 
have  each  alternately  7  and  8  links. 

Total  number  of  wires  in  each  cable :  At  the  tower,  18,400;  solid  metal  section, 
975  square  inches ;  ultimate  strength,  87,700  tons.  At  the  dip,  16,900 ;  solid  metal  sec- 
tion, 890  square  inches;  ultimate  strength,  80,000  tons. 

The  dip  of  the  cables  is  one-tenth  of  the  span,  310  feet. 

The  cables  are  so  arranged  that  for  an  addition  of  6  tracks  (to  a  total  of  14)  the 
wires  in  each  cable  can  be  increased  in  the  future  up  to  25,000  by  the  addition  of 
wire  links. 

The  chains  of  wire  links  are  surrounded  by  a  water-tight  removable  shell  (or 
envelope)  of  corrugated  steel  (one-eighth  inch  thick)  9  feet  in  diameter,  as  a  pro- 
tection against  the  weather. 

The  bracing  between  the  cables  is  of  rolled  steel. 

The  verticals  consist  of  two  latticed  20-inch  eyebars,  varying  in  cross  section  for 
one  member  from  140  to  80  square  inches. 


78 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


The  diagonals  consist  of  sets  of  adjustable  rods,  from  2  to  3  inches  square,  with 
screw  ends  fitting  into  eyebar  saddles,  having  their  bearings  on  the  cable  pins  of  the 
middle  chain.  The  aggregate  section  of  the  square  rods  varies  for  one  member  from 
206  to  92  square  inches. 

The  average  weight  per  linear  foot  of  each  suspended  rib,  including  wire  links, 
steel  shoes,  pins,  and  steel  envelope,  is  7,200  pounds;  bracing  between  cables,  1,300 
pounds;  total  net  weight  of  one  rib  average  per  linear  foot,  8,500  pounds. 

Conrpared  with  one  of  the  four  arch  ribs  of  St.  Louis  bridge:  Steel  tube  flanges, 
635  pounds  average  per  linear  foot;  web,  285  pounds  average  per  linear  foot;  total, 
920  pounds. 

Or,  compared  with  one  of  the  six  arch  ribs  of  the  Harlem  bridge :  Flanges,  850 
pounds  average ;  web,  190  pounds  average ;  total,  1,040  pounds. 

In  the  St.  Louis  bridge  the  web  is  30  per  cent  of  the  total  weight  of  the  rib ;  in 
the  Washington  bridge,  19  per  cent,  and  in  the  North  River  bridge  only  15  per  cent 
of  the  total  weight  of  the  rib. 

The  two  ribs  can  resist  a  bending  moment  of  1,600,000  foot  tons  before  the  perma- 
nent tension  in  the  upper  cables  from  the  dead  load  would  be  nullified.  (Wire-link 
cables  can  not  take  compression,  and  overstraining  from  bending  is  next  to  impos- 
sible). 

Calculation  shows  that  to  produce  this  bending  moment  trains,  would  be  required 
side  by  side,  1,200  feet  long,  aggregating  10,800  tons  moving  over  the  bridge. 

It  would  be  next  to  impossible  to  bring  such  a  load  and  such  an  extraordinary 
assemblage  of  double-headed  trains  upon  the  bridge. 

The  assistance  of  the  stiffening  trusses  is  here  entirely  disregarded,  also  that  part 
of  the  live  load  directly  absorbed  by  the  cables  by  reason  of  their  deflection. 

The  calculated  maximum  deflection,  at  one  quarter  the  span,  from  this  extreme 
load  is  2.4  feet.  In every-day  operation  the  load  effects  and  deflection  will  probably 
not  reach  10  per  cent  of  this  extreme. 

The  suspended  ribs,  with  a  depth  of  one  fifty-sixth  of  the  span,  are  therefore  stiff 
and  strong  enough  to  resist  deformation,  without  stiffening  trusses,  from  the  heaviest 
moving  load,  and  being  in  stable  equilibrium  are  more  rigid  than  the  compression 
ribs  with  fixed  ends  of  the  St.  Louis  arch  bridge  with  a  depth  of  one  forty-fourth  of 
the  span,  which  are  in  unstable  equilibrium  and  subject  to  compression  and  tension 
alternately. 

The  suspended  ribs  are  assumed  to  be  hinged  at  their  ends  in  the  a-  chorages  and 
on  the  towers.  This  assumption  is  severely  carried  out  in  the  construction.  The 
exact  equivalent  for  the  hinge  on  the  towers  is  a  toggle  joint,  made  of  short  wire 
links. 

The  diagonals  of  the  cable  bracing  during  erection  remain  loose.  After  erection 
of  complete  superstructure,  and  with  the  cables  therefor  in  perfect  equilibrium 
from  dead  load,  equally  divided  upon  the  four  cables,  the  diagonals  are  adjusted 
and  receive  a  slight  initial  tension. 

The  cable  bearings  on  the  towers  are  fixed,  i.  e.,  can  not  slide,  but  they  can  accom- 
modate themselves  to  the  hinge  movement  of  the  toggle  joint.  The  bending  strains 
in  the  towers  (from  the  difference  of  temperature,  and  from  load  effects  in  the 
cables)  are  allowed  for. 

The  temperature  strains  in  the  cables  are  relatively  small.  The  steel  envelopes 
protect  the  wires  against  the  direct  rays  of  the  sun  and  against  uneven  heating. 

The  bending  moments  from  live  load  in  the  long  end  spans  (having  a  dip  of  g^) 

would  be  greater  than  in  the  middle  span. 

To  reduce  them  to  the  same  limit,  the  end  spans  are  in  the  middle  provided  with 
anchor  columns,  reaching  to  masonry  pedestals  below.  These  columns  bear  no  part 
of  the  dead  load.  They  are  counterwoighted  in  the  pedestals  in  such  manner  as  to 
be  affected  only  by  an  excessive  concentrated  live  load,  in  which  case  a  positive  or 
negative  reaction  (of  -J-  6,000  tons,  according  to  position  of  live  load)  is  produced 
and  accurately  known.  The  computation  of  the  bending  strains  is  thereby  much 
facilitated. 

(Note. — This  is  the  present  arrangement,  but  a  change  to  a  fixed  hinge,  as  more 
economical  still,  is  under  consideration). 

The  weight  per  linear  foot  of  the  suspended  structure  in  the  end  spans  is  brought 
within  the  same  limits  as  for  the  middle  span. 

The  position  of  the  anchorages  and  lengths  of  end  spans  are  dictated  by  local  con- 
ditions. If  the  anchorages  could  have  been  placed  nearer  to  the  lowers  it  would 
have  reduced  cost  of  bridge  very  much,  as  shown  below. 

The  arch  ribs  are  cradled  6.5  per  cent,  i.  e.,  inclined  toward  each  other.  They  are 
160  feet  apart  on  top  of  towers  and  120  feet  at  the  middle  of  span, 

No  wind  bracing  is  required  between  the  cradled  cables. 

The  suspenders  are  of  bundled  steel  wire  ropes,  35  square  inches  solid  section. 
Maximum  tension,  with  14  tracks,  on  one  suspender,  700  tone. 


BRIDGE  ACROSS  THE  HUDSON  RIVER.  79 

Assuming  E  ==  29,000,000,  the  middle  span  would  deflect  under  the  assumed  maxi- 
mum load  of  12  tons  per  linear  toot,  which  may  never  occur. 

From  elongation  of  cables  in  middle  span  inches..  48 

From  bending  of  towers  do  21 

From  -j-  65c  F.,  as  a  maximum,  affecting  only  the  middle  span  do  21.7 


Maximum  deflection  do  90.7 

Normal  camber  15  feet=180.0  iuches  for  middle  temperature  at +  50°  F. 

Pounds  per 
square  inch. 

Tension  in  the  cable  wires  from  dead  load  alone   32,  500 

From  temperature  bending  moment   6,  200 

From  full  live  load  (12  tons  per  linear  foot)   2G,  000 


Maximum  at  center  of  span   64,  700 

Maximum  from  bending  moment  at  the  quarter   65,000 

Lowest  elastic  limit  of  180,000  pounds  steel  wire  assumed  at   85,  000 

But  more  likely  to  run  up  to  120,000 


The  maximum  dellection,  at  the  quarter  from  one-sided  loading,  of  29  inches  is 
equal  to  a  change  of  six-tenths  per  cent  in  the  grade  on  the  middle  span. 

Track  platform  and  wind  girders. — The  panels  are  50  feet  long.  Stringers  placed 
directly  under  the  rails,  which  rest  on  wooden  block  cushions  between  steel  guard 
rails,  open  on  the  sides  to  let  cinder  and  snow  fall  through;  no  wooden  ties  at  all 
are  used. 

The  space  between  steel  guard  rails  is  stretched  over  with  a  taut  wire  netting, 
weighing  2±  pounds  per  square  foot. 

Stringers  and  floor  beams,  5  feet  deep,  dimensioned  for  locomotives  weighing  150 
tons  with  tendor. 

The  lower  floor  beam  carries  8  tracks,  and  has  3  intermediate  supports  from  a 
cross  arch  above,  for  which  it  acts  as  the  tension  member  between  arch  footings. 

The  cross  arch  is  65  feet  high  and  placed  at  every  panel  point.  It  acts  also  as 
cross  bracing  between  the  lower  and  upper  wind  trusses. 

The  cross  arch  is  further  to  carry  an  upper  floor  beam  for  a  second  deck  of  6 
rapid-transit  tracks  to  be  added  when  needed  in  the  future. 

On  top  of  the  cross  arch  is  the  promenade,  20  feet  wide  with  wooden  flooring. 

The  lower  wind  truss  is  in  the  plane  of  the  lower  floor  for  8  tracks.  The  upper 
wind  truss  is  placed  below  the  promenade.  Both  are  115  wide,  center  to  center  of 
chords,  equal  to  one-twenty-sixth  of  the  distance  between  the  towers. 

Both  wind  trussed  have  the  same  chord  sections  (180  square  inches  each  for  100,000 
pounds  steel)  from  end  to  end  (anchorage  to  anchorage). 

The  wind  trusses  are  proportioned  as  horizontal  continuous  girders  of  uniform 
chord  section,  with  a  consequent  great  saving  of  metal  for  the  chords.  Their  ends 
in  the  towers  can  slide  and  adjust  themselves  to  temperature  changes,  but  are 
arranged  to  resist  vertical  and  horizontal  bending  moments  at  the  towers. 

The  ends  of  the  wind  trusses  at  the  anchorages  are  firmly  anchored  into  the 
masonry,  to  also  resist  end-bending  moments. 

The  assumed  wind  pressure  is  2,400  pounds  per  linear  foot  of  superstructure. 

Maximum  stress  in  chord  -|-  36,000  pounds  per  square  inch  and  maximum  stress 
in  diagonals  -f-  30,000  pounds  per  square  inch  from  maximum  wind  pressure. 

The  chord  sections  of  the  horizontal  wind  trusses  are  utilized  also  in  two  vertical 
stiffening  trusses,  in  connection  with  the  floor  system  and  cross  arches,  as  an  aid  in 
distributing  the  concentrated  train  loads  upon  the  braced  cables,  although  not  nec- 
essary, as  stated  above. 

The  cable  ribs  are  so  rigid  that  the  aid  of  the  vertical  trusses  amounts  to  only  10 
per  cent;  i.  e..  00  per  cent of  the  deforming  effect  from  moving  load  goes  into  the  arch 
ribs  and  10  per  cent  into  the  stiffening  trusses  for  equal  values  of  deflection. 

Erection. — The  construction  of  the  anchorages  and  the  erection  of  the  steel  Lowers 
oiler  no  new  features,  except  large  size. 

All  steel  work,  except  wire  loops,  can  be  done  with  existing  plant.  The  plant  for 
making  wire  loops  will  be  simple  and  not  expensive.  There  will  be  9,300  wire  links, 
and  it  is  estimated  that  on  one  machine  two  links  can  be  furnished  per  day  on  an 
average,  which  would  require  sixteen  mouths  on  ten  machines  for  the  9,300  links 
required. 

As  for  manufacturing  capacity  of  wire,  there  are  several  large  works  equipped 
for  it,  and  one  of  them  offers  to  alone  furnish  all  the  wire  (over  40,000  tons)  in  one 
year  without  extra  effort. 

The  links  will  average  4  tons  each,  and  the  cost  of  making  the  links  is  estimated 
at  live-eighths  cent  per  pound,  including  oiling.    (The  wires  will  not  be  galvanized). 

The  erection  of  the  superstructure  will  be  similar  to  that  for  the  Brooklyn  bridge, 
S.  Ex.  1  11 


80 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


i.  c,  without  false  works.  First,  a  temporary  footbridge  of  wire  ropes  over  the 
towers,  strong  enough  to  carry  one  set  of  wire  links  of  permanent  cables. 

Then,  erection  of  first  wire  links,  suspended  temporarily  from  the  footbridge 
above,  alternating  one  and  two  links,  commencing  at  each  tower,  toward  center 
and  anchorage,  respectively,  until  first  set  of  wire  links  is  connected  up  from  anchor- 
age to  anchorage  for  each  side.  Thereon  all  following  wire  links  are  erected  and 
pushed  upon  the  pins  wi-thout  further  support  from  the  footbridge.  The  wire  ropes 
of  temporary  footbridge  are  used  afterwards  for  the  suspenders. 

The  wire  links,  being  all  made  in  the  shop  to  exact  length,  the  same  as  eyebars, 
the  erection  of  the  cables  can  proceed  without  regard  to  the  weather  and  without 
delay  from  adjustment;  160  erecting  gangs,  if  needed,  can  be  employed  at  one  time 
simultaneously  in  the  erection  of  the  four  cables,  which  can  be  completed  in  less 
than  ten  months. 

The  erection  of  the  other  parts  of  the  superstructure  is  the  same  as  for  Brooklyn 
bridge. 

It  is  immaterial  what  form  the  cables  assume  during  erection.  The  adjustment  of 
the  diagonal  bracing  between  the  cables  and  of  stiffening  trusses  takes  place  only 
after  the  entire  superstructure  down  to  the  rails  is  in  place. 

The  time  of  construction  is  estimated  at  four  years,  namely,  two  years  for  anchor- 
ages and  tower  bases,  nine  months  for  steel  towers,  and  fifteen  months  for  cables 
and  superstructure. 

Weights  of  superstructure,  6,800  feet  long,  between  anchorages: 

(1)  8  tracks: 

100-pound  rails  on  wooden  blocks. 
Steel  guard  rails  and  wire  netting. 

Tons. 

200  pounds  per  linear  foot  of  track   5,440 

(2)  Floor  construction,  per  panel  of  50  feet : 

Tons. 

8  pairs  of  stringers     88 

1  cross  arch,  with  suspended  floor  beam,  including  verticals 

for  stiffening  trusses   73 

2  sets  of  hanger  eyebars  fo^  cable  suspenders   7 

4  wind  chords   65 

Horizontal  wind  bracing  (average)   12 

Stringers  and  hand  rail  for  promenade   7 

Diagonals  of  stiffening  trusses  (average)   8 

Total  per  panel   260 

Tons. 

Per  linear  foot  of  bridge,  5.2  tons   35,360 

(3)  Suspenders  of  wire  ropes   1, 900 

(4)  Two  cable  ribs: 

Cables  with  pins,  shoes,  couplings,  and  shell   48,  960 

Bracing  between  cables  *   8,  840 

  57,  800 

Weight  of  superstructure,  metal   95,  060 

Weight  of  superstructure,  niefcal  and  track   100,  500 

Average  dead  load  of  superstructure,  per  linear  foot  of—  .  . 

Metal   13.95 

Track  80 

Flooring  of  promenade  > 

Telegraph  wires  \ 

15.  00 

°g  — ^^'=1.875  tons  dead  load  per  linear  foot  of  track,  which  is  the  same  as 

for  a  400-foot  Whipple  truss  span. 
Total  amount  of  steel  in — 

Tons 

Anchorages   12,  400 

Towers   24,  780 

Superstructure   95,060 

132,  240 

iqo  04.0 

Weight  of  steel  per  linear  foot  of  entire  bridge,  7,340  feet  long:  =18.02 
Ions,  or  2.25  tons  per  linear  foot  of  track. 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


81 


The  addition  of  six  rapid-transit  tracks  (for  a  live  load  of  1  ton  per  linear  foot  of 
track),  whenever  needed  in  the  future,  will  require  17,500  tons  wire  links  and 
10,200  tons  of  other  steel  work,  27,700  tons,  total  addition,  at  a  cost  of  $2,500,000. 

If  the  bridge  had  been  located  at  souie  point  north,  Avhere  the  rocky  binds  come 
close  to  the  river,  the  length  would  have  been  reduced  to  about  5,500  feet,  a  saving 
iu  length  of  over  1,800  feet. 

For  suspension  spans  of  3,000  feet,  a  difference  of  200  feet  more  or  less  spau  does 
not  greatly  affect  the  cost  per  running  foot. 

The  cost  of  bridge  would  have  been  reduced : 

(1)  In  the  anchorages,  on  account  of  the  natural  rock  bluffs,  at  least         $1,  000,  000 

(2)  In  the  towers,  probably  nothing. 

(3)  In  the  superstructure,  1,800  feet  shorter,  about   2,  200,  000 


3, 200,  000 

Hence  the  bridge  for  eight  tracks  would  then  have  cost  only  about  $17,800,000. 

There  is,  however,  an  offset  of  1,800  feet  approaches  against  such  saving,  which,  at 
$400  a  linear  foot,  would  cost  $720,000,  thus  making  the  saving  only  about •$2,480,000. 

Six  per  cent  interest  thereon  would  have  amounted  to  $148,800  yearly. 

The  location  at  Hoboken  holds  out  the  certainty  of  greater  revenue,  from  local 
traffic  alone,  by  ten  times  the  amount  of  the  interest  on  the  saving  in  cost  of  a  shorter 
and  cheaper  location  further  north. 

The  cost  of  the  land,  of  the  approaches,  and  of  the  terminal  station  are  greater 
than  the  cost  of  the  bridge.  There  is,  further,  the  interest  account  during  construc- 
tion and  the  legal  and  administration  expenses. 

July  18,  1894.  G.  L. 


Appendix  E. 

THEORY  OF  THE  CONTINUOUS  STIFFENING  TRUSS  WITH  ENDS  ANCHORED  DOWN  BUT 
NOT  FIXED  IN  A  VERTICAL  PLANE. 

The  ends  of  this  stiffening  truss  are  free  to  change  their  direction,  but  not  their 
elevation,  in  a  vertical  plane,  and  the  truss  is  continuous  from  end  to  end.  The 
theory  of  this  truss  has  been  published  for  a  considerable  number  of  years  in 
standard  engineering  works,  and  its  principal  formulas  only  will  be  given  without 
detailed  denionstjation : 


The  moving  load  will  be  taken  as  passing  on  the  span  from  the  left  end  A 
Reference  will  be  made  to  Fig.  1  in  the  analysis  and  the  following  notation  will  be 
employed : 

Length  of  stiffening  truss  between  centers  of  end  supports   /  (feet) 

Moving  load  per  linear  foot   w 

Uniform  upward  pull  (supposed  to  bo  distributed  over  I)  per  linear  foot   p 

Reaction  of  truss  at  A  (upward  under  conditions  taken)   R 

Reaction  of  truss  at  B  (downward  under  conditions  taken)   R1 

Tho  coordinate  of  x  or  X\  will  be  measured  from  A  as  an  origin  positive  toward 
C,  the  center  of  the  span.  In  general,  bending  moments  will  be  represented  by  M 
and  shears  by  S. 

In  this  case  all  the  moving  load  is  carried  to  the  cable  through  the  suspenders; 
hence  the  two  reactions  R  and  R1  will  be  equal  and  opposite  in  direction. 

S.  Ex.  12  6 


82  BRIDGE  ACROSS  THE  HUDSON  RIVER. 

The  equations  of  condition  for  equilibrium  are: 

R  +pl  —wxj + R*  —  0   (1) 

£of  pP  +  Rll— i  wx,a  =  0   (2) 

R+Ri  =  0   (3) 

Equation  (1)  at  once  gives: 

WX\ 

V=  I    (4) 

Then  from  equations  (2)  and  (3) : 

B  =  -B'=~!(i_*')   (5) 

The  bending  moment  at  any  section  distant  x  (never  greater  than  Xi)  from  A  is: 

M  =  Bx-(«-j>)f (l-*)   (6) 

Heuce  there  is  always  a  point  of  contra-flexure  at  the  head  of  the  moving  load. 

M  has  its  maximum  value  for  x  =  ^. 

2 

Hence : 

Mi  =  wxS  fl-*S   (7) 


Mi  has  its  maximum  value  for  Xi  =  ~  I. 

o 

Hence : 

TV/T  4     Wl2  /Q\ 

Mmax=27   8  (8) 


The  unloaded  part  of  the  span  acts  aa  a  beam  simply  supported  at  its  ends  and 
carrying  an  upward  load  of  uniform  intensity  p  =  Hence  its  greatest  bending 

moment  at  center  will  be : 

-M'=^J0-*')2  (9) 

2 

This  has  its  maximum  for  x{  =-^l. 

o 

Hence : 

-M       =  4   wP  .   (10) 

max    27  8 

If  any  given  length  of  load,  as  ivxl}  move  over  the  span,  there  will  be  a  point  of 
contra-flexure  at  each  extremity  of  it,  and  the  greatest  bendiug  moment  it  produces 
(i.  e.,  at  its  center)  will  be  given  in  general  by  equation  (7),  or  by  equation  (8)  if 

2 

its  length  is  —  I.    The  range  of  the  maximum  downward  bending  moment  given  by 

o 

equation  (8)  is  the  middle  third  of  the  span,  while  the  same  maximum,  as  an  upward 
moment,  equation  (10),  occurs  at  the  one-third  points  only. 

The  shear  at  any  section  distant  x  (less  than  x{)  from  A  (figure  1),  is: 


=  R+  px  —  wx  =  w(l  —        Q1  —   -'  (11) 


BRIDGE  ACROSS  THE  PIUDSON  RIVER.  83 

When  x=0  (i.  e.,  at  the  end  of  the  span)  the  shear  is  equal  to  the  reaction  R. 
The  greatest  shear  is  found  by  making  x=0  and  X\  =  ^  in  equation  (11) :  —  S  max= 

~.  When  x  is  greater  thanf1,  the  shear  S  becomes  negative  and  takes  its  inaxi- 
o  2 

mum  at  the  head  of  the  load,  or  for  x  =  Xi : 

S==— ™*  A  —  ^)=Ri   (12) 

Equations  (11)  and  (12)  give  the  shear  when  the  load  wxi  occupies  any  position 
on  the  span,  provided  x  and  X\  are  measured  from  either  end  of  that  loading. 
The  shear  in  tho  unloaded  portion  of  the  span  (I  —  x{)  is: 

S  =  -Ri-M'-*)  =  '-fi{  (*-*-) -2(1_l)  (I3) 

This  expression  attains  its  maximum  values  for  x  —  l  and  x=xi}  as  it  then  becomes 
equal  to  R  or  R1 ;  it  also  becomes  zero  for  x  =  $  (I 


THEORY   OP  THE  CENTER  HINGED  STIFFENING  TRUSS. 

There  will  be  given  in  this  appendix  only  such  a  concise  statement  of  the  theory 
of  the  center-hinged  stiffening  truss  as  the  purposes  of  this  report  require,  but 
within  those  limits  it  will  be  complete.  Those  purposes  are  satisfactorily  served  by 
considering  tho  question  as  a  problem  in  statics,  in  which  tho  effects  resulting  from 
the  deformation  of  the  cablo,  the  elastic  stretching  of  the  suspenders,  and  the  elas- 
tic deflection  of  tho  truss,  all  under  the  moving  load,  are  ignored.  A  complete 
analysis  of  tho  influences  of  these  separate  assumptions  exerted  upon  the  results 
obtained  would  be  out  of  place  here,  although  the  effect  of  the  stretching  of  tho 
suspenders  is  illustrated  at  tho  end  of  this  appendix,  but  it  may  bo  stated  that  the 
resultant  effect  is  to  confer  upon  the  cable  an  increased  facility  of  adjustment  in 
form  to  tho  requirements  of  a'varying  moving  load,  and  hence,  an  enhanced  capac- 
ity to  receive  such  moving  load  directly  through  the  suspenders  without 
action  of  the  truss.  The  variations  from  tho  exact  treatment  which  involves  tho 
consideration  of  plastic  deformation  of  tho  members  named  results  in  formulae 
which,  as  the  mathematical  theory  of  tho  combined  elastic  action  of  cables  and 
beams  show,  give  greater  bending'moments  and  shears  in  the  stiffening  truss  over 
the  greater  part  of  the  span  than  those  which  actually  exist.  All  estimates  of 
material  for  tho  members  affected  will  consequently  bo  on  the  safe  side.  The 
influence  of  the  elevation  or  depression  of  the  cablo  as  a  whole,  due  either  to  a 
variation  in  temperature  or  to  elastic  extension,  is  eliminated  by  the  center  hinge. 


The  moving  load  will  be  taken  on  the  left  half  truss  A  C,  and  the  same  notation 
as  that  given  below  fig.  1  in  tho  preceding  section  will  bo  used. 

Case  I. 

In  this  case  tho  moving  load  w  will  bo  taken  as  passing  on  tho  truss  from  A  and 
its  variable  length  measured  from  that  point  will  be  represented  by  x\. 

Inasmuch  as  the  pull  exerted  on  the  truss  by  the  suspenders  is  upward  and  as  there 
is  no  moving  load  on  B  C,  it  is  clear  that  the  reaction  R1  at  B  must  bo  downward  in 
direction  and  that  an  equal  downward  reaction  must  bo  exerted  by  the  half  truss  A 
CouBC  at  C,  the  hinge  point  at  tho  center  of  the  span.  That  downward  reaction 
at  C  is  a  part  of  the  requisite  portion  of  tho  moving  load  w  X\  determined  by  the 

simple  principle  of  the  lever  applied  toAC=  s  as  a  span,  while  tho  other  part  of 


84 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


that  portion  is  carried  directly  to  A  without  exerting  any  pull  on  the  suspenders,  and, 
consequently,  without  stressing  the  cable.  The  part  transferred  to  C  (equal  to  the 
downward  reaction  at  13)  is  evidently  less  than  that  transferred  to  A,  except  in  the 
case  of  the  moving  load  covering  the  half  span,  when  they  are  equal.  From  this 
reasoning  it  follows  that  the  total  upward  pull  on  the  suspenders  is  less  than  the 
moving  load  iv  Xibj  the  excess  of  the  part  transferred  to  C,  but  both  these  differ- 
ences disappear  when  the  moving  load  covers  the  half  span. 

The  forces  acting  on  the  entire  truss  A  13  are,  then,  the  upward  reaction  R  (at  A), 
the  downward  reaction  R1  (at  B),  the  upward  pull  pi,  and  the  downward-moving 
load  w  X\}  and  it  is  necessary  for  equilibrium  that  their  sum  shall  be  zero. 

Hence : 

2>l-\-R  —  wxi — R!=0  (14) 

Because  the  truss  is  hinged  at  the  point  C,  moments  of  the  same  forces  acting  on 
each  half,  and  about  C  as  a  center,  must  be  equal  to  zero. 
Hence : 


8  +  2  ~wx>  (^-)-°  { 
8"      2  j 


By  placing  the  two  equations  (15)  equal  to  each  other 

R  =  w  Xi—^—R1  (16) 

The  substitution  of  this  value  of  R  in  equation  (14)  will  give: 

By  the  combination  of  the  second  of  equations  (15)  and  equation  (17) : 


B'=^  (18) 

By  placing  this  value  of  R1  in  equation  (16) : 

R=WXl(i_|i)  :  d9) 

The  value  of  R1  from  equation  (18)  placed  in  the  second  of  equations  (15)  will 
yield : 

„-2tv2Cl  (20^ 

P—  p 

Those  values  of  Rl,  R,  and  p,  in  which  xv  must  never  exceed  £  I,  will  enable  all 
moments  and  shears  to  bo  immediately  written. 

The  expression  for  the  bending  moment  at  any  point  x  (not  greater  than  xt)  from 
tho  point  of  support  A  is : 


M 


In  order  to  determine  what  position  of  loading  must  be  taken  so  that  the  maxi- 
mum bending  moment  will  exist  at  any  desired  section  distant  x  from  the  point  of 
support  A,  the  first  derivative  of  M  in  respect  to  Xi  (x  being  considered  constant) 
must  be  put  equal  to  zero  and  then  solved  for  X\ : 


d  M        <       3X&    3xiX  |^ 2x^x^  ?  __n 


3Z— 2x 


(22) 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


85 


By  placing  the  value  of  X\  in  equation  (21) : 


Equation  (23)  will  give  the  greatest  possible  bending  moment  in  the  half  truss 
A  C  at  any  point  indicated  or  located  by  the  coordinate  x  which  will  never  exceed 
I 

-Tp  The  corresponding  length  ot  loading  from  A  will  be  given  bya?i  in  equation  (22). 
The  greatest  bending  moment  in  the  half  truss  A  C  can  be  found  by  placing 
^x  =  0,  then  solving  this  ( 
there  is  a  simple  procedure. 


*Pj^x  -    0,  then  solving  this  equation  for  x  and  placing  its  value  in  equation  (23) ;  but 


Let  X\  be  considered  constant  in  equation  (21),  then  if  0  there  will  be  located 

the  section  of  the  greatest  bending  for  any  given  length  of  loading  x, : 

dM.        i     s       3#i\      s2xr     „  \  ) 

♦'•^^(t-1) (24) 
2xi8 
P  ~~ 1 

If  this  value  of  x  be  placed  in  equation  (22)  there  will  result: 

Equation  (25)  is  satisfied,  for: 

^  =  .395---<*  (26) 

Or,  the  greatest  bending  moment  in  the  span  occurs  when  0.395  of  its  length  is 
covered  with  the  moving  load. 

If  j  is  taken  from  equation  (26)  and  placed  in  equation  (24) : 

x  =.234 1   (27) 

Equation  (27)  thus  locates  the  section  of  greatest  bonding  in  the  span. 
By  placing  £  =  .234  I  in  equation  (23),  that  maximum  moment  becomes: 

wl1 

M    ■  =.018825  —  wF-=:  .1506  -«   (28) 

max  o 

The  half  truss  B  C  is  simply  supported  at  each  end  and  carries  the  uniform  upward 
load  p  por  linear  foot;  hence  it  will  be  bent  upward  with  the  negative  moment: 

This  expression  evidently  has  its  maximum  value  when  X\.  — 

a 

Hence : 


M 


max 


=-tG1-»)  ^ 


I 

In  these  expressions  neither  xt  norx  can  ever  exceed 


86 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


With  the  value  x  =  —  I : 
4 

max         g    8  64  " W 

The  shear  at  any  section  located  by  the  coordinate  x  (never  exceeding  xx)  is: 

S=j>«  +  B—  ,ra=  ^g"-'  +  «*,  (>-§■)- «*. 
...S=,ra(2^-1)  +  Wx,(l-^  (31) 

In  order  to; determine  the  greatest  shear  at  any  point  or  section  x  the  same  pro- 
cedure employed  lor  the  moment  must  be  followed: 

dS  =  4««,  3x,=0  .%_P    (82) 

rfxi  Z  3Z  — 4z  v  y 

This  value  of  sc,  placed  in  equation  (31)  gives: 

^="\m£=m-*\ (33) 

The  value  Si  in  equation  (33)  gives  the  greatest  shear  in  the  half  truss  at  any  sec- 
tion x. 

The  form  of  equation  (33)  shows  that  the  maximum  of  all  the  values  of  Si  will  be 
found  by  making  x  =  0;  hence: 

Sma*  =  T ' (34) 

By  making  x  =  0  in  equation  (32)  it  appears  that  the  length  of  moving  load 
required  to  produce  the  maximum  shear  is : 

*i=!    (35) 

This  value  of  X\  placed  in  equation  (19)  shows  that  the  maximum  shear  is  equal  to 
the  maximum  reaction  R. 

The  preceding  equations  have  been  so  written  that  an  upward  shear  is  positive 
and  a  downward  shear  negative.  If  Si  be  placed  equal  to  zero,  by  using  equation 
(33): 

The  second  value  indicates  nothing  useful,  but  the  first  value  (^^)  shows  that  the 

shear  is  always  upward  over  that  quarter  of  the  span  nearest  A,  and  downward  or 
negative  over  that  quarter  adjacent  to  C.    The  greatest  negative  shears  will 
obviously  occur  at  the  head  of  the  moving  load,  and  they  will  be  given  by  making 
x=x}  in  equation  (31); 

_S,='i|L2  (?£'-|)  (37) 

For  a  maximum : 

x,=^an.l-S,  =  -'| 
The  preceding  reasoning  shows  that  the  maximum  negative  shears  will  he  given  hy 
equation  (37)  in  which  X\  must  have  values  hetween  -|  and^  only;  but  that  the  maxi- 
mum positive  shears  will  he  given  hy  equation  (33),  in  which  x  must  have  values  hetween 

x  =  0  and  x=  \  only. 

4 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


87 


Since  forxi^-^,  IV  =  l(^  and  })  =  ™  ,  the  expression  for  the  shear  in  the  half 
truss  B  C  (or  in  the  half  truss  A  C  fully  loaded)  will  bo: 


S1  ==  w 


G-f)  <*» 


By  increasing  r  from  0  to  \  in  equation  (38)  there  will  result  the  positivo  shears 

a 

iii  iho  right  half  of  B  C  and  the  negative  shears  in  the  left  half  of  B  C. 

Case  II. 

In  this  case  a  moving  load  of  length  varying  from  0  to  A  will  be  supposed  to  be 

placed  on  tlie  span  and  to  extend  from  the  center  C  to  any  point  distant  ^  -  \  _ 

from  C.    All  notation  will  remain  as  in  Case  I. 

The  equations  of  condition  for  equilibrium  corresponding  to  equations  (14)  and 
( 15)  now  become : 

jri-f  ^ _ w  {1  _  jbA—  Ri  =  0   (39) 

+  2-2  (2-^)"  =°1  


pi-  R1/ 
8-2-  =0 


(40) 


The  two  equations  (10)  give: 

„        W/  i  \  2 

R  =  l\2~x0  -R'   (41) 

The  substitutions  of  R  from  equation  (41)  and  pi  from  the  second  of  equations 
(40)  in  equation  (24)  give: 

R,-l(l*^)  (t  +  §)    (42> 

By  placing  this  value  of  R1  in  equation  (41) : 

w  si        \  si      3x, \ 
*=2\2-x0  V2--TJ   (43> 

The  same  value  of  R1  in  the  second  of  equations  (40) : 

2w  s  I 


2w  s  I        \  sx\     1  \ 


(44) 


The  reactions  R  and  R1  will  evidently  have  their  greatest  values  when  X\  =  0: 


R        =Ri        =^   (45) 

max         max  8 

The  greatest  values  of  two  bending  moments  must  be  determined — i.  e.,  one  at 
that  extremity  of  the  moving  load  at  the  distance  X\,  from  A,  fig.  2,  and  the  other 
at  any  point  of  A  C  with  that  half  span  entirely  covered  with  the  moving  load. 
The  expression  for  the  moment  at  any  point  x  between  the  end  A  and  aj  is : 

M=Rx+i       G-*.) f f 0- f0+?(?  +1)  1  m 

The  form  of  this  expression  shows  it  to  bo  a  maximum  for  x  =  xx : 

M,  =  h'Xi  I  (J-*)'  (47) 


88         '  BRIDGE  ACROSS  THE  HUDSON  RIVER. 

In  order  to  find  a  maximum  : 


dM 


Hence  Xi 


Which  placed  in  equation  (47) 


Mi 


wf  27 
8  "512 


0527 


wl1 


(48) 


If  the  moving  load  covers  the  whole  of  the  half  span  A  C,  the  moment  at  any 
point  x  will  he,  since  then  p  =  1~\ 


M-  =  (,-^2(^-x)  =  ^(^-x) 


(49) 


This  is  the  maximum  for#  = 


M] 


125  wl 


64" 


(50) 


The  bending  in  the  right  half  of  the  span  is  given  by  equations  (29)  and  (30)  in 
the  preceding  case. 

The  general  expression  for  the  upward  (positive)  shear  in  the  unloaded  portion  Xi 
of  £he  left  half,  A  C,  of  the  span  is  : 


For  the  greatest  value  of  S,  always  x  =  X\: 


(51) 
(52) 


The  shears  in  each  half  of  the  span  with  the  left  half,  A  C,  fully  loaded,  have  been 
given  in  the  preceding  case  by  equation  (38). 

EFFECT  OF  CHANGES  OF  LENGTHS  OF  THE  SUSPENDERS  ON  THE  DISTRIBUTIVE  FUNC- 
TION OF  THE  STIFFENING  GIRDER. 

The  suspenders  are  lengthened  or  shortened  by  changes  of  temperature ;  they  are 
lengthened  by  the  live  load;  their  increment  of  length  due  to  either  cause  are  pro- 


Fig.3. 

i 
i 

-  C  — -f 

^ —  i 

1 

k  \  \~ 

 -i<fe 

r  s 

i 

i  - 

portional  to  their  length ;  these  increments  are,  therefore,  ordinates  of  parabolas. 

Referring  to  fig.  3,  whore  A  C  B  represents  the  cable,  acb  the  stiffening  girder,  and 
Aa,B6,  the  towers,  if  the  increments  of  length  of  the  suspenders,  due  to  a  rise  of  tern- 


BRIDGE  ACROSS  THE  HUDSON  RIVER. 


89 


peraturc,  be  plotted  downward  from  lino  a  b,  they  will  give  the  parabolic  arc  a(  Oi ; 
supposing  that  the  towers  expand  in  the  same  proportion  as  the  suspenders,  the 
curve  «]  Oi  becomes  a  o2  and  represents,  in  position,  the  deflected  line  of  the  girder, 
this  line  is  similar  to  the  curve  of  deflection  due  to  a  uniform  rate  of  loading,  and 
has  a  slight  convexity  upward,  showing  that  no  disturbance  has  taken  place  in  the 
distributive  action  of  the  girder,  except  a  slight  relief  of  duty  for  the  loaded  part, 
and  a  slight  increase  of  duty  for  the  unloaded  part,  of  the  girder.  Owing,  however, 
to  the  greater  bulk  of  material  in  the  tower,  its  temperature  and  rate  of  expansion 
will  be  less  than  for  the  suspenders;  if  a  s  represents  the  difference  due  to  this 
cause,  then  the  curve,  a  o2  drops  to  the  position  s  o3,  and  «So3  becomes  the  line  of 
deflection  of  the  girder,  showing  that  in  the  immediate  vicinity  of  the  towers  the 
suspenders  are  partly  relieved  of  their  duty,  and  that  a  part  of  the  load  is  carried 
directly  to  the  tower  by  the  girder. 

A  similar  construction  for  a  fall  of  temperature,  to  the  right  of  the  figure,  shows 
the  effect  on  the  girder  to  be  slight  deflection  downward  with  the  convexity  of  the 
curve  downward,  indicating  a  slight  increase  of  duty  for  the  loaded  part  of  the 
girder  and  a  slight  decrease  for  the  unloaded  part,  owing  to  the  difference  of  con- 
traction b  t  of  the  tower,  the  deflected  line  of  the  girder  will  be  b  T  m>,  showing  that 
the  duty  of  the  suspenders  in  the  immediate  vicinity  of  the  tower  has  been  increased. 

The  effect  of  the  elastic  elongation  of  the  suspenders  due  to  the  live  load  is  exactly 
the  same  as  it  is  for  a  rise  of  temperature,  except  that  owing  to  the  fact  that  the 
tower  contracts  instead  of  expanding,  the  disturbing  effects  in  the  vicinity  of  the 
tower  is  increased  in  warm  weather  and  decreased  in  cold  weather. 

The  ill  effects  on  the  girders  and  suspenders  arising  from  these  disturbances  are 
avoided  by  omitting  the  suspenders  for  a  short  distance  next  to  the  towers. 

c 


NEW  YORK  &  NEW  JERSEY  BRIDGE. 
PROFILE  OF  HUDSON  RIVER  ON  LINE  "A" 
BETWEEN    59™  &  60™   STS.  PRODUCED 


SEx  t3-      53  ; 


|-;jl!;ill!f;[[lii[tH 


Pt#A/ Of  Prl/D&f 


/?/>/><?/ astso  u/vaf/?  /7c r  or  Cbv&ttss  frr&orto  Jva/s7-/S9* 


Srwt 300/'/' "  / /M 

\      ■!»    A,    A,  *L — d..    «t.  iU — »l.  ,i„ 


g  E,   /2.      53  3 


I 


Sketch    of  Towers 


SEx  53 


